Geng, Xianguo; Jia, Minxin; Xue, Bo; Zhai, Yunyun Application of tetragonal curves to coupled Boussinesq equations. (English) Zbl 07812612 Lett. Math. Phys. 114, No. 1, Paper No. 30, 42 p. (2024). MSC: 37K10 37K20 14H42 37K40 PDFBibTeX XMLCite \textit{X. Geng} et al., Lett. Math. Phys. 114, No. 1, Paper No. 30, 42 p. (2024; Zbl 07812612) Full Text: DOI
Geng, Xianguo; Wang, Jia; Wang, Kedong; Li, Ruomeng Soliton resolution for the complex short-pulse positive flow with weighted Sobolev initial data in the space-time soliton regions. (English) Zbl 07801715 J. Differ. Equations 386, 214-268 (2024). Reviewer: Eugene Postnikov (Kursk) MSC: 35Q51 35Q15 37K15 35C08 35C20 35B40 78A60 30E15 41A60 PDFBibTeX XMLCite \textit{X. Geng} et al., J. Differ. Equations 386, 214--268 (2024; Zbl 07801715) Full Text: DOI
Geng, Xianguo; Liu, Wenhao; Li, Ruomeng Long-time asymptotics for the coupled complex short-pulse equation with decaying initial data. (English) Zbl 07801712 J. Differ. Equations 386, 113-163 (2024). MSC: 35Q15 35Q55 35Q41 35Q60 78A60 37K15 37K35 35C08 35B40 35P25 41A60 PDFBibTeX XMLCite \textit{X. Geng} et al., J. Differ. Equations 386, 113--163 (2024; Zbl 07801712) Full Text: DOI
Zhai, Yunyun; Hu, Xinghua; Ji, Ting; Wei, Jiao; Li, Yihao Localized wave solutions to the vector nonlinear Schrödinger equation with nonzero backgrounds. (English) Zbl 07789833 Math. Methods Appl. Sci. 46, No. 16, 17328-17344 (2023). MSC: 35Q55 35Q51 37K40 37K10 PDFBibTeX XMLCite \textit{Y. Zhai} et al., Math. Methods Appl. Sci. 46, No. 16, 17328--17344 (2023; Zbl 07789833) Full Text: DOI
Liu, Wei; Geng, Xianguo Quasi-periodic solutions to a hierarchy of integrable nonlinear differential-difference equations. (English) Zbl 1527.35339 Math. Methods Appl. Sci. 46, No. 8, 8728-8745 (2023). MSC: 35Q51 37K10 37K20 PDFBibTeX XMLCite \textit{W. Liu} and \textit{X. Geng}, Math. Methods Appl. Sci. 46, No. 8, 8728--8745 (2023; Zbl 1527.35339) Full Text: DOI
Yan, Feiying; Geng, Xianguo; Li, Ruomeng Spectral and soliton structures for the four-component Kaup-Newell type negative flow equation. (English) Zbl 1527.35195 Commun. Nonlinear Sci. Numer. Simul. 126, Article ID 107462, 17 p. (2023). MSC: 35Q15 35C08 35K10 35K15 PDFBibTeX XMLCite \textit{F. Yan} et al., Commun. Nonlinear Sci. Numer. Simul. 126, Article ID 107462, 17 p. (2023; Zbl 1527.35195) Full Text: DOI
Lou, Yu; Zhang, Wenyun; Zhang, Yi; Xu, Guoan Hybrid structures of localized waves for the coupled extended mKdV equation. (English) Zbl 1524.35543 Wave Motion 120, Article ID 103142, 15 p. (2023). MSC: 35Q53 35C08 PDFBibTeX XMLCite \textit{Y. Lou} et al., Wave Motion 120, Article ID 103142, 15 p. (2023; Zbl 1524.35543) Full Text: DOI
Xu, Siqi A coupled complex mKdV equation and its N-soliton solutions via the Riemann-Hilbert approach. (English) Zbl 1522.35453 Bound. Value Probl. 2023, Paper No. 83, 12 p. (2023). MSC: 35Q53 35Q15 35C08 37K10 37K15 PDFBibTeX XMLCite \textit{S. Xu}, Bound. Value Probl. 2023, Paper No. 83, 12 p. (2023; Zbl 1522.35453) Full Text: DOI
Li, Ruomeng; Geng, Jingru; Geng, Xianguo Rogue-wave and breather solutions of the Fokas-Lenells equation on theta-function backgrounds. (English) Zbl 07708824 Appl. Math. Lett. 142, Article ID 108661, 8 p. (2023). MSC: 35Q55 35C08 37K35 14H25 PDFBibTeX XMLCite \textit{R. Li} et al., Appl. Math. Lett. 142, Article ID 108661, 8 p. (2023; Zbl 07708824) Full Text: DOI
Li, Ruomeng; Geng, Xianguo Rogue waves and breathers of the derivative Yajima-Oikawa long wave-short wave equations on theta-function backgrounds. (English) Zbl 07707930 J. Math. Anal. Appl. 527, No. 1, Part 1, Article ID 127399, 26 p. (2023). MSC: 35Q53 35Q51 35C08 37K10 37K35 33E05 15A18 11F50 11F27 PDFBibTeX XMLCite \textit{R. Li} and \textit{X. Geng}, J. Math. Anal. Appl. 527, No. 1, Part 1, Article ID 127399, 26 p. (2023; Zbl 07707930) Full Text: DOI
Zhai, Yunyun; Wei, Lifei; Geng, Xianguo; Tao, Lei Breather solutions to the AB system with non-zero background. (English) Zbl 1518.35211 J. Geom. Phys. 190, Article ID 104858, 15 p. (2023). MSC: 35C08 35G61 35Q15 37K40 PDFBibTeX XMLCite \textit{Y. Zhai} et al., J. Geom. Phys. 190, Article ID 104858, 15 p. (2023; Zbl 1518.35211) Full Text: DOI
Geng, Xianguo; Zeng, Xin Algebro-geometric quasi-periodic solutions to the Satsuma-Hirota hierarchy. (English) Zbl 1519.37081 Physica D 448, Article ID 133738, 12 p. (2023). Reviewer: Ahmed Lesfari (El Jadida) MSC: 37K10 37K20 14H70 14K20 PDFBibTeX XMLCite \textit{X. Geng} and \textit{X. Zeng}, Physica D 448, Article ID 133738, 12 p. (2023; Zbl 1519.37081) Full Text: DOI
Geng, Xue; Guan, Liang Algebro-geometric solutions of the sine-Gordon hierarchy. (English) Zbl 1509.37088 J. Nonlinear Math. Phys. 30, No. 1, 114-134 (2023). MSC: 37K10 37K20 14H70 PDFBibTeX XMLCite \textit{X. Geng} and \textit{L. Guan}, J. Nonlinear Math. Phys. 30, No. 1, 114--134 (2023; Zbl 1509.37088) Full Text: DOI
Liu, Wenhao; Geng, Xianguo; Wang, Kedong; Chen, Mingming Spectral analysis and long-time asymptotics for the Harry Dym-type equation with the Schwartz initial data. (English) Zbl 1512.35423 J. Differ. Equations 357, 181-235 (2023). MSC: 35Q15 35Q53 35B40 41A60 PDFBibTeX XMLCite \textit{W. Liu} et al., J. Differ. Equations 357, 181--235 (2023; Zbl 1512.35423) Full Text: DOI
Li, Ruomeng; Geng, Xianguo Periodic-background solutions of Kadomtsev-Petviashvili I equation. (English) Zbl 1509.35267 Z. Angew. Math. Phys. 74, No. 2, Paper No. 68, 15 p. (2023). MSC: 35Q53 37K10 37K15 35K35 35C08 PDFBibTeX XMLCite \textit{R. Li} and \textit{X. Geng}, Z. Angew. Math. Phys. 74, No. 2, Paper No. 68, 15 p. (2023; Zbl 1509.35267) Full Text: DOI
Geng, Xianguo; Liu, Wenhao; Wang, Kedong; Chen, Mingming Long-time asymptotics for the complex nonlinear transverse oscillation equation. (English) Zbl 1507.35131 Anal. Appl., Singap. 21, No. 2, 497-533 (2023). MSC: 35Q15 35Q74 74K10 74Q10 74B20 41A60 35B05 35B40 PDFBibTeX XMLCite \textit{X. Geng} et al., Anal. Appl., Singap. 21, No. 2, 497--533 (2023; Zbl 1507.35131) Full Text: DOI
Liu, Zhifeng; Wang, Yuezhen; Dong, Xiangmin; Zhang, Caixia; Li, Ying A novel model for evaluating preload based on spectral problem in system with double-bolted connections. (English) Zbl 1525.74004 Appl. Math. Modelling 102, 21-34 (2022). MSC: 74A10 PDFBibTeX XMLCite \textit{Z. Liu} et al., Appl. Math. Modelling 102, 21--34 (2022; Zbl 1525.74004) Full Text: DOI
Zhai, Yunyun; Wei, Lifei; Geng, Xianguo; Wei, Jiao Multi-bright-dark soliton solutions to the \(AB\) system in nonlinear optics. (English) Zbl 1514.35387 Commun. Theor. Phys. 74, No. 4, Article ID 045003, 8 p. (2022). MSC: 35Q51 35Q15 35C08 78A60 PDFBibTeX XMLCite \textit{Y. Zhai} et al., Commun. Theor. Phys. 74, No. 4, Article ID 045003, 8 p. (2022; Zbl 1514.35387) Full Text: DOI
Wei, Jiao; Geng, Xianguo; Wang, Xin; Zhai, Yunyun Finite genus solutions of the generalized Merola-Ragnisco-Tu lattice hierarchy. (English) Zbl 1509.37093 J. Math. Phys. 63, No. 8, Article ID 083503, 21 p. (2022). MSC: 37K10 37K20 35Q53 35Q51 PDFBibTeX XMLCite \textit{J. Wei} et al., J. Math. Phys. 63, No. 8, Article ID 083503, 21 p. (2022; Zbl 1509.37093) Full Text: DOI
Xu, Xiaoxue; Cao, Cewen; Zhang, Da-jun Algebro-geometric solutions to the lattice potential modified Kadomtsev-Petviashvili equation. (English) Zbl 1511.37090 J. Phys. A, Math. Theor. 55, No. 37, Article ID 375201, 28 p. (2022). MSC: 37K60 37K10 37K20 37K35 39A36 PDFBibTeX XMLCite \textit{X. Xu} et al., J. Phys. A, Math. Theor. 55, No. 37, Article ID 375201, 28 p. (2022; Zbl 1511.37090) Full Text: DOI arXiv
Chen, Ming Ming; Geng, Xian Guo; Wang, Ke Dong Spectral analysis and long-time asymptotics for the coherently-coupled nonlinear Schrödinger system. (English) Zbl 1503.35206 Acta Math. Sin., Engl. Ser. 38, No. 11, 2090-2114 (2022). MSC: 35Q55 35Q41 35Q15 35B40 37K15 41A60 PDFBibTeX XMLCite \textit{M. M. Chen} et al., Acta Math. Sin., Engl. Ser. 38, No. 11, 2090--2114 (2022; Zbl 1503.35206) Full Text: DOI
Jia, Minxin; Geng, Xianguo; Wei, Jiao Algebro-geometric quasi-periodic solutions to the Bogoyavlensky lattice 2(3) equations. (English) Zbl 07615128 J. Nonlinear Sci. 32, No. 6, Paper No. 98, 34 p. (2022). MSC: 37K60 37K10 37K20 14H42 14H70 PDFBibTeX XMLCite \textit{M. Jia} et al., J. Nonlinear Sci. 32, No. 6, Paper No. 98, 34 p. (2022; Zbl 07615128) Full Text: DOI
Chen, Mingming; Geng, Xianguo; Wang, Kedong; Xue, Bo Application of the nonlinear steepest descent method to the general coupled nonlinear Schrödinger system. (English) Zbl 1501.35367 Commun. Pure Appl. Anal. 21, No. 9, 3171-3191 (2022). MSC: 35Q55 35Q41 35Q15 35B40 37K15 41A60 PDFBibTeX XMLCite \textit{M. Chen} et al., Commun. Pure Appl. Anal. 21, No. 9, 3171--3191 (2022; Zbl 1501.35367) Full Text: DOI
Wang, Kedong; Geng, Xianguo; Chen, Mingming; Li, Ruomeng Spectral analysis and long-time asymptotics of a coupled nonlinear Schrödinger system. (English) Zbl 1498.35517 Bull. Malays. Math. Sci. Soc. (2) 45, No. 5, 2071-2106 (2022). MSC: 35Q55 35B40 35Q53 35Q15 35P99 41A60 PDFBibTeX XMLCite \textit{K. Wang} et al., Bull. Malays. Math. Sci. Soc. (2) 45, No. 5, 2071--2106 (2022; Zbl 1498.35517) Full Text: DOI
Wang, Kedong; Geng, Xianguo; Chen, Mingming Riemann-Hilbert approach and long-time asymptotics of the positive flow short-pulse equation. (English) Zbl 1501.35277 Physica D 439, Article ID 133383, 27 p. (2022). MSC: 35Q15 35B40 35B09 35C08 41A60 35P30 45D05 PDFBibTeX XMLCite \textit{K. Wang} et al., Physica D 439, Article ID 133383, 27 p. (2022; Zbl 1501.35277) Full Text: DOI
He, Guoliang; Zhai, Yunyun; Zheng, Zhenzhen Algebro-geometric integration of a modified shallow wave hierarchy. (English) Zbl 07565157 Int. J. Nonlinear Sci. Numer. Simul. 23, No. 3-4, 401-417 (2022). MSC: 37K40 37K20 14H42 PDFBibTeX XMLCite \textit{G. He} et al., Int. J. Nonlinear Sci. Numer. Simul. 23, No. 3--4, 401--417 (2022; Zbl 07565157) Full Text: DOI
Chen, Mingming; Geng, Xianguo; Wang, Kedong Long-time asymptotics for the modified complex short pulse equation. (English) Zbl 1494.35032 Discrete Contin. Dyn. Syst. 42, No. 9, 4439-4470 (2022). MSC: 35B40 35Q15 35Q51 PDFBibTeX XMLCite \textit{M. Chen} et al., Discrete Contin. Dyn. Syst. 42, No. 9, 4439--4470 (2022; Zbl 1494.35032) Full Text: DOI
Geng, Xianguo; Wei, Jiao Three-sheeted Riemann surface and solutions of the Itoh-Narita-Bogoyavlensky lattice hierarchy. (English) Zbl 1498.37112 Rev. Math. Phys. 34, No. 4, Article ID 2250009, 27 p. (2022). MSC: 37K60 37K10 37K20 14H42 14H70 39A36 PDFBibTeX XMLCite \textit{X. Geng} and \textit{J. Wei}, Rev. Math. Phys. 34, No. 4, Article ID 2250009, 27 p. (2022; Zbl 1498.37112) Full Text: DOI
Geng, Xianguo; Li, Ruomeng; Xue, Bo A vector Geng-Li model: new nonlinear phenomena and breathers on periodic background waves. (English) Zbl 1490.35093 Physica D 434, Article ID 133270, 11 p. (2022). MSC: 35C08 35Q51 35Q55 37K10 PDFBibTeX XMLCite \textit{X. Geng} et al., Physica D 434, Article ID 133270, 11 p. (2022; Zbl 1490.35093) Full Text: DOI
Wang, Kedong; Geng, Xianguo; Chen, Mingming; Xue, Bo Riemann-Hilbert approach and long-time asymptotics for the three-component derivative nonlinear Schrödinger equation. (English) Zbl 1489.35176 Anal. Math. Phys. 12, No. 3, Paper No. 71, 33 p. (2022). MSC: 35Q15 35B40 35Q55 41A60 PDFBibTeX XMLCite \textit{K. Wang} et al., Anal. Math. Phys. 12, No. 3, Paper No. 71, 33 p. (2022; Zbl 1489.35176) Full Text: DOI
Lou, Yu; Zhang, Yi; Ye, Rusuo Higher-order semi-rational solutions for the coupled complex modified Korteweg-de Vries equation. (English) Zbl 1484.35330 Math. Model. Nat. Phenom. 17, Paper No. 4, 15 p. (2022). MSC: 35Q51 37K40 74H05 PDFBibTeX XMLCite \textit{Y. Lou} et al., Math. Model. Nat. Phenom. 17, Paper No. 4, 15 p. (2022; Zbl 1484.35330) Full Text: DOI
Geng, Xianguo; Wang, Jia; Xue, Bo Riemann-Hilbert approach and \(N\)-soliton solutions for a negative matrix AKNS system with a Hermitian symmetric space. (English) Zbl 1524.35117 Wave Motion 108, Article ID 102838, 10 p. (2022). MSC: 35C08 35Q15 35Q53 PDFBibTeX XMLCite \textit{X. Geng} et al., Wave Motion 108, Article ID 102838, 10 p. (2022; Zbl 1524.35117) Full Text: DOI
Wang, Xiu-Bin; Han, Bo The general fifth-order nonlinear Schrödinger equation with nonzero boundary conditions: inverse scattering transform and multisoliton solutions. (English. Russian original) Zbl 1486.81103 Theor. Math. Phys. 210, No. 1, 8-30 (2022); translation from Teor. Mat. Fiz. 210, No. 1, 11-37 (2022). MSC: 81Q05 35Q55 81U40 35C08 35Q15 35G31 70H33 81Q80 PDFBibTeX XMLCite \textit{X.-B. Wang} and \textit{B. Han}, Theor. Math. Phys. 210, No. 1, 8--30 (2022; Zbl 1486.81103); translation from Teor. Mat. Fiz. 210, No. 1, 11--37 (2022) Full Text: DOI arXiv
Wu, Jianping \(N\)-soliton, \(M\)-breather and hybrid solutions of a time-dependent Kadomtsev-Petviashvili equation. (English) Zbl 07478786 Math. Comput. Simul. 194, 89-96 (2022). MSC: 35-XX 37-XX PDFBibTeX XMLCite \textit{J. Wu}, Math. Comput. Simul. 194, 89--96 (2022; Zbl 07478786) Full Text: DOI
Jia, Minxin; Geng, Xianguo; Zhai, Yunyun; Wei, Jiao; Liu, Huan Analytic Riemann theta function solutions of coupled Korteweg-de Vries hierarchy. (English) Zbl 1484.14068 East Asian J. Appl. Math. 11, No. 4, 732-754 (2021). Reviewer: Ahmed Lesfari (El Jadida) MSC: 14H42 35Q55 35Q51 37K10 35Q53 35L65 PDFBibTeX XMLCite \textit{M. Jia} et al., East Asian J. Appl. Math. 11, No. 4, 732--754 (2021; Zbl 1484.14068) Full Text: DOI
Zhao, Qiulan; Yang, Qianqian; Qu, Xiangwen Characters of explicit solutions for a semidiscrete integrable coupled equation. (English) Zbl 1481.39018 Adv. Math. Phys. 2021, Article ID 9964540, 10 p. (2021). MSC: 39A36 37K60 PDFBibTeX XMLCite \textit{Q. Zhao} et al., Adv. Math. Phys. 2021, Article ID 9964540, 10 p. (2021; Zbl 1481.39018) Full Text: DOI
Zhai, Yunyun; Ji, Ting; Geng, Xianguo Coupled derivative nonlinear Schrödinger III equation: Darboux transformation and higher-order rogue waves in a two-mode nonlinear fiber. (English) Zbl 1510.35318 Appl. Math. Comput. 411, Article ID 126551, 14 p. (2021). MSC: 35Q55 35C08 37K35 PDFBibTeX XMLCite \textit{Y. Zhai} et al., Appl. Math. Comput. 411, Article ID 126551, 14 p. (2021; Zbl 1510.35318) Full Text: DOI
Jia, Minxin; Geng, Xianguo; Wei, Jiao; Zhai, Yunyun; Liu, Huan Coupled discrete Sawada-Kotera equations and their explicit quasi-periodic solutions. (English) Zbl 1479.35722 Anal. Math. Phys. 11, No. 4, Paper No. 140, 26 p. (2021). MSC: 35Q51 37K10 35B10 35B40 PDFBibTeX XMLCite \textit{M. Jia} et al., Anal. Math. Phys. 11, No. 4, Paper No. 140, 26 p. (2021; Zbl 1479.35722) Full Text: DOI
Xue, Bo; Du, Huiling; Geng, Xianguo A Degasperis-Procesi equation II with multi-peakon solutions. (English) Zbl 1481.37078 Appl. Math. Lett. 121, Article ID 107463, 7 p. (2021). MSC: 37K10 37K40 35Q51 PDFBibTeX XMLCite \textit{B. Xue} et al., Appl. Math. Lett. 121, Article ID 107463, 7 p. (2021; Zbl 1481.37078) Full Text: DOI
Xiao, Yu; Fan, Engui; Liu, Pan Inverse scattering transform for the coupled modified Korteweg-de Vries equation with nonzero boundary conditions. (English) Zbl 1486.35368 J. Math. Anal. Appl. 504, No. 2, Article ID 125567, 31 p. (2021). MSC: 35Q53 35Q15 37K15 35B40 35C08 35C09 PDFBibTeX XMLCite \textit{Y. Xiao} et al., J. Math. Anal. Appl. 504, No. 2, Article ID 125567, 31 p. (2021; Zbl 1486.35368) Full Text: DOI arXiv
Geng, Xianguo; Liu, Wei; Xue, Bo Explicit solutions of the coupled Bogoyavlensky lattice 1(2) Hierarchy. (English) Zbl 1473.35478 Result. Math. 76, No. 2, Paper No. 67, 27 p. (2021). MSC: 35Q51 37K10 37K60 37K35 37K20 35C20 14H42 PDFBibTeX XMLCite \textit{X. Geng} et al., Result. Math. 76, No. 2, Paper No. 67, 27 p. (2021; Zbl 1473.35478) Full Text: DOI
Chen, Mingming; Geng, Xianguo; Wang, Kedong Spectral analysis and long-time asymptotics for the potential Wadati-Konno-Ichikawa equation. (English) Zbl 1470.37093 J. Math. Anal. Appl. 501, No. 2, Article ID 125170, 27 p. (2021). MSC: 37K40 37K35 35B40 PDFBibTeX XMLCite \textit{M. Chen} et al., J. Math. Anal. Appl. 501, No. 2, Article ID 125170, 27 p. (2021; Zbl 1470.37093) Full Text: DOI
Wang, Kedong; Chen, Mingming; Li, Ruomeng; Geng, Xianguo An integrable generalized Korteweg-de Vries equation with pseudo-peakons. (English) Zbl 1462.35342 Appl. Math. Lett. 115, Article ID 106942, 9 p. (2021). MSC: 35Q53 35C08 35B07 35B09 37K10 PDFBibTeX XMLCite \textit{K. Wang} et al., Appl. Math. Lett. 115, Article ID 106942, 9 p. (2021; Zbl 1462.35342) Full Text: DOI
Ji, Ting; Zhai, Yunyun Soliton, breather and rogue wave solutions of the coupled Gerdjikov-Ivanov equation via Darboux transformation. (English) Zbl 1516.37115 Nonlinear Dyn. 101, No. 1, 619-631 (2020). MSC: 37K40 37K35 35Q51 35C08 PDFBibTeX XMLCite \textit{T. Ji} and \textit{Y. Zhai}, Nonlinear Dyn. 101, No. 1, 619--631 (2020; Zbl 1516.37115) Full Text: DOI
Wang, Kedong; Geng, Xianguo; Chen, Mingming; Li, Ruomeng Long-time asymptotics for the generalized Sasa-Satsuma equation. (English) Zbl 1484.35340 AIMS Math. 5, No. 6, 7413-7437 (2020). MSC: 35Q53 35B40 PDFBibTeX XMLCite \textit{K. Wang} et al., AIMS Math. 5, No. 6, 7413--7437 (2020; Zbl 1484.35340) Full Text: DOI
Li, Yihao; Li, Ruomeng; Xue, Bo; Geng, Xianguo A generalized complex mKdV equation: Darboux transformations and explicit solutions. (English) Zbl 1524.35542 Wave Motion 98, Article ID 102639, 13 p. (2020). MSC: 35Q53 35A30 35L65 37K10 PDFBibTeX XMLCite \textit{Y. Li} et al., Wave Motion 98, Article ID 102639, 13 p. (2020; Zbl 1524.35542) Full Text: DOI
Zhai, Yunyun; Geng, Xianguo; Xue, Bo Riemann theta function solutions to the coupled long wave-short wave resonance equations. (English) Zbl 1482.35199 Anal. Math. Phys. 10, No. 4, Paper No. 82, 25 p. (2020). Reviewer: Solomon Manukure (Austin) MSC: 35Q51 35Q55 37K10 37K20 35C20 14H42 PDFBibTeX XMLCite \textit{Y. Zhai} et al., Anal. Math. Phys. 10, No. 4, Paper No. 82, 25 p. (2020; Zbl 1482.35199) Full Text: DOI
Wang, Jingqun; Tian, Lixin; Guo, Boling; Zhang, Yingnan Nonlinear stability of breather solutions to the coupled modified Korteweg-de Vries equations. (English) Zbl 1450.35237 Commun. Nonlinear Sci. Numer. Simul. 90, Article ID 105367, 13 p. (2020). MSC: 35Q53 35C08 37K40 37K10 35B35 35P99 PDFBibTeX XMLCite \textit{J. Wang} et al., Commun. Nonlinear Sci. Numer. Simul. 90, Article ID 105367, 13 p. (2020; Zbl 1450.35237) Full Text: DOI
Ye, Rusuo; Zhang, Yi; Zhang, Qinyu; Chen, Xiaotong Vector rational and semi-rational rogue wave solutions in the coupled complex modified Korteweg-de Vries equations. (English) Zbl 1524.35566 Wave Motion 92, Article ID 102425, 10 p. (2020). MSC: 35Q53 76B15 37K10 PDFBibTeX XMLCite \textit{R. Ye} et al., Wave Motion 92, Article ID 102425, 10 p. (2020; Zbl 1524.35566) Full Text: DOI
Chen, Jinbing Quasi-periodic solutions of the negative-order Jaulent-Miodek hierarchy. (English) Zbl 1441.35210 Rev. Math. Phys. 32, No. 3, Article ID 2050007, 46 p. (2020). MSC: 35Q51 37K10 37K20 35B10 PDFBibTeX XMLCite \textit{J. Chen}, Rev. Math. Phys. 32, No. 3, Article ID 2050007, 46 p. (2020; Zbl 1441.35210) Full Text: DOI arXiv
Shen, Jing; Geng, Xianguo; Xue, Bo Modulation instability and dynamics for the Hermitian symmetric space derivative nonlinear Schrödinger equation. (English) Zbl 1473.35515 Commun. Nonlinear Sci. Numer. Simul. 78, Article ID 104877, 16 p. (2019). MSC: 35Q55 35L65 35C08 35Q82 37K10 81Q05 82D10 PDFBibTeX XMLCite \textit{J. Shen} et al., Commun. Nonlinear Sci. Numer. Simul. 78, Article ID 104877, 16 p. (2019; Zbl 1473.35515) Full Text: DOI
Geng, Xianguo; Shen, Jing; Xue, Bo Dynamical behaviour of rogue wave solutions in a multi-component AB system. (English) Zbl 1524.35505 Wave Motion 89, 1-13 (2019). MSC: 35Q51 35A30 35L65 37K10 PDFBibTeX XMLCite \textit{X. Geng} et al., Wave Motion 89, 1--13 (2019; Zbl 1524.35505) Full Text: DOI
Geng, Xianguo; Wei, Jiao; Zeng, Xin Algebro-geometric integration of the modified Belov-Chaltikian lattice hierarchy. (English. Russian original) Zbl 1429.37041 Theor. Math. Phys. 199, No. 2, 675-694 (2019); translation from Teor. Mat. Fiz. 199, No. 2, 235-256 (2019). MSC: 37K20 37K10 14H70 PDFBibTeX XMLCite \textit{X. Geng} et al., Theor. Math. Phys. 199, No. 2, 675--694 (2019; Zbl 1429.37041); translation from Teor. Mat. Fiz. 199, No. 2, 235--256 (2019) Full Text: DOI
Geng, Xianguo; Zeng, Xin; Wei, Jiao The application of the theory of trigonal curves to the discrete coupled nonlinear Schrödinger hierarchy. (English) Zbl 1421.35335 Ann. Henri Poincaré 20, No. 8, 2585-2621 (2019). Reviewer: Eugene Postnikov (Kursk) MSC: 35Q55 35Q41 37K10 35Q51 35C08 PDFBibTeX XMLCite \textit{X. Geng} et al., Ann. Henri Poincaré 20, No. 8, 2585--2621 (2019; Zbl 1421.35335) Full Text: DOI
Geng, Xianguo; Chen, Mingming; Wang, Kedong Long-time asymptotics of the coupled modified Korteweg-de Vries equation. (English) Zbl 1420.35313 J. Geom. Phys. 142, 151-167 (2019). MSC: 35Q53 35B40 37K15 35Q15 41A60 65J15 PDFBibTeX XMLCite \textit{X. Geng} et al., J. Geom. Phys. 142, 151--167 (2019; Zbl 1420.35313) Full Text: DOI
Geng, Xianguo; Liu, Wei; Xue, Bo Finite genus solutions to the coupled Burgers hierarchy. (English) Zbl 1407.35171 Result. Math. 74, No. 1, Paper No. 11, 28 p. (2019). MSC: 35Q51 35Q55 37K10 37K20 PDFBibTeX XMLCite \textit{X. Geng} et al., Result. Math. 74, No. 1, Paper No. 11, 28 p. (2019; Zbl 1407.35171) Full Text: DOI
Ma, Wen-Xiu The inverse scattering transform and soliton solutions of a combined modified Korteweg-de Vries equation. (English) Zbl 1412.35380 J. Math. Anal. Appl. 471, No. 1-2, 796-811 (2019). Reviewer: Ti-Jun Xiao (Fudan) MSC: 35R30 PDFBibTeX XMLCite \textit{W.-X. Ma}, J. Math. Anal. Appl. 471, No. 1--2, 796--811 (2019; Zbl 1412.35380) Full Text: DOI
Wei, Jiao; Geng, Xianguo; Zeng, Xin The Riemann theta function solutions for the hierarchy of Bogoyavlensky lattices. (English) Zbl 1403.37078 Trans. Am. Math. Soc. 371, No. 2, 1483-1507 (2019). MSC: 37K10 37K20 14H42 37K40 14H70 PDFBibTeX XMLCite \textit{J. Wei} et al., Trans. Am. Math. Soc. 371, No. 2, 1483--1507 (2019; Zbl 1403.37078) Full Text: DOI
Geng, Xianguo; Zhai, Yunyun; Xue, Bo; Wei, Jiao A hierarchy of long wave-short wave type equations: quasi-periodic behavior of solutions and their representation. (English) Zbl 1417.37252 J. Nonlinear Math. Phys. 26, No. 1, 1-23 (2019). MSC: 37K40 37K20 14H42 PDFBibTeX XMLCite \textit{X. Geng} et al., J. Nonlinear Math. Phys. 26, No. 1, 1--23 (2019; Zbl 1417.37252) Full Text: DOI
Cheng, Wenguang; Xu, Tianzhou Consistent Riccati expansion solvable classification and soliton-cnoidal wave interaction solutions for an extended Korteweg-de Vries equation. (English) Zbl 07822189 Chin. J. Phys., Taipei 56, No. 6, 2753-2759 (2018). MSC: 35Qxx 37Kxx 35Cxx PDFBibTeX XMLCite \textit{W. Cheng} and \textit{T. Xu}, Chin. J. Phys., Taipei 56, No. 6, 2753--2759 (2018; Zbl 07822189) Full Text: DOI
Geng, Xianguo; Zeng, Xin; Wei, Jiao Riemann surface and Riemann theta function solutions of the discrete integrable hierarchy. (English) Zbl 1442.37081 Chaos Solitons Fractals 116, 365-375 (2018). MSC: 37K20 30F30 PDFBibTeX XMLCite \textit{X. Geng} et al., Chaos Solitons Fractals 116, 365--375 (2018; Zbl 1442.37081) Full Text: DOI
Geng, Xianguo; Shen, Jing; Xue, Bo A new nonlinear wave equation: Darboux transformation and soliton solutions. (English) Zbl 1465.35349 Wave Motion 79, 44-56 (2018). MSC: 35Q51 35C05 35C08 37K10 35L65 PDFBibTeX XMLCite \textit{X. Geng} et al., Wave Motion 79, 44--56 (2018; Zbl 1465.35349) Full Text: DOI
Hu, Bei-Bei; Xia, Tie-Cheng; Ma, Wen-Xiu Riemann-Hilbert approach for an initial-boundary value problem of the two-component modified Korteweg-de Vries equation on the half-line. (English) Zbl 1427.35232 Appl. Math. Comput. 332, 148-159 (2018). MSC: 35Q53 35Q15 PDFBibTeX XMLCite \textit{B.-B. Hu} et al., Appl. Math. Comput. 332, 148--159 (2018; Zbl 1427.35232) Full Text: DOI
Tian, Shou-Fu Initial-boundary value problems for the coupled modified Korteweg-de Vries equation on the interval. (English) Zbl 1397.35262 Commun. Pure Appl. Anal. 17, No. 3, 923-957 (2018). MSC: 35Q53 35Q51 35Q15 41A60 35B40 35P20 37K15 PDFBibTeX XMLCite \textit{S.-F. Tian}, Commun. Pure Appl. Anal. 17, No. 3, 923--957 (2018; Zbl 1397.35262) Full Text: DOI
Zeng, Xin; Geng, Xianguo Finite-band solutions for the hierarchy of coupled Toda lattices. (English) Zbl 1385.37075 Acta Appl. Math. 154, No. 1, 59-81 (2018). MSC: 37J35 14H70 34K17 PDFBibTeX XMLCite \textit{X. Zeng} and \textit{X. Geng}, Acta Appl. Math. 154, No. 1, 59--81 (2018; Zbl 1385.37075) Full Text: DOI
Chen, Jinbing Quasi-periodic solutions to a negative-order integrable system of 2-component KdV equation. (English) Zbl 1387.35515 Int. J. Geom. Methods Mod. Phys. 15, No. 3, Article ID 1850040, 34 p. (2018). MSC: 35Q51 35Q53 37K10 37K20 70K43 35B10 PDFBibTeX XMLCite \textit{J. Chen}, Int. J. Geom. Methods Mod. Phys. 15, No. 3, Article ID 1850040, 34 p. (2018; Zbl 1387.35515) Full Text: DOI
Wu, Jianping; Geng, Xianguo Inverse scattering transform and soliton classification of the coupled modified Korteweg-de Vries equation. (English) Zbl 1510.35281 Commun. Nonlinear Sci. Numer. Simul. 53, 83-93 (2017). MSC: 35Q53 37K15 37K40 PDFBibTeX XMLCite \textit{J. Wu} and \textit{X. Geng}, Commun. Nonlinear Sci. Numer. Simul. 53, 83--93 (2017; Zbl 1510.35281) Full Text: DOI
Ma, Wen-Xiu Trigonal curves and algebro-geometric solutions to soliton hierarchies. II. (English) Zbl 1404.35393 Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 473, No. 2203, Article ID 20170233, 20 p. (2017). MSC: 35Q53 35C08 35Q51 37K10 14H70 14H42 PDFBibTeX XMLCite \textit{W.-X. Ma}, Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 473, No. 2203, Article ID 20170233, 20 p. (2017; Zbl 1404.35393) Full Text: DOI
Ma, Wen-Xiu Trigonal curves and algebro-geometric solutions to soliton hierarchies. I. (English) Zbl 1404.35392 Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 473, No. 2203, Article ID 20170232, 20 p. (2017). MSC: 35Q53 35C08 35Q51 37K10 14H70 14H42 PDFBibTeX XMLCite \textit{W.-X. Ma}, Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 473, No. 2203, Article ID 20170232, 20 p. (2017; Zbl 1404.35392) Full Text: DOI arXiv
Li, Zhu Algebro-geometric solutions of the Harry Dym hierarchy. (English) Zbl 1401.37076 Int. J. Nonlinear Sci. Numer. Simul. 18, No. 2, 129-136 (2017). MSC: 37K10 14H70 14H42 14H50 35Q53 37K20 PDFBibTeX XMLCite \textit{Z. Li}, Int. J. Nonlinear Sci. Numer. Simul. 18, No. 2, 129--136 (2017; Zbl 1401.37076) Full Text: DOI
Geng, Xianguo; Zeng, Xin Application of the trigonal curve to the Blaszak-Marciniak lattice hierarchy. (English. Russian original) Zbl 1382.37076 Theor. Math. Phys. 190, No. 1, 18-42 (2017); translation from Teor. Mat. Fiz. 190, No. 1, 21-47 (2017). MSC: 37K20 37K10 37K60 14H70 PDFBibTeX XMLCite \textit{X. Geng} and \textit{X. Zeng}, Theor. Math. Phys. 190, No. 1, 18--42 (2017; Zbl 1382.37076); translation from Teor. Mat. Fiz. 190, No. 1, 21--47 (2017) Full Text: DOI
Tian, Shou-Fu Initial-boundary value problems of the coupled modified Korteweg-de Vries equation on the half-line via the Fokas method. (English) Zbl 1377.37100 J. Phys. A, Math. Theor. 50, No. 39, Article ID 395204, 32 p. (2017). Reviewer: Guido Schneider (Stuttgart) MSC: 37K10 35Q53 35Q15 PDFBibTeX XMLCite \textit{S.-F. Tian}, J. Phys. A, Math. Theor. 50, No. 39, Article ID 395204, 32 p. (2017; Zbl 1377.37100) Full Text: DOI
Geng, Xianguo; Zeng, Xin Quasi-periodic solutions of the Belov-Chaltikian lattice hierarchy. (English) Zbl 1408.37123 Rev. Math. Phys. 29, No. 8, Article ID 1750025, 27 p. (2017). MSC: 37K20 37K40 14H42 37K10 14H70 PDFBibTeX XMLCite \textit{X. Geng} and \textit{X. Zeng}, Rev. Math. Phys. 29, No. 8, Article ID 1750025, 27 p. (2017; Zbl 1408.37123) Full Text: DOI
Zhai, Yunyun; Geng, Xianguo The coupled Sasa-Satsuma hierarchy: trigonal curve and finite genus solutions. (English) Zbl 1376.37113 Anal. Appl., Singap. 15, No. 5, 667-697 (2017). MSC: 37K20 37K40 14H42 37K10 14H70 PDFBibTeX XMLCite \textit{Y. Zhai} and \textit{X. Geng}, Anal. Appl., Singap. 15, No. 5, 667--697 (2017; Zbl 1376.37113) Full Text: DOI
Geng, Xianguo; Wu, Jianping Riemann-Hilbert approach and \(N\)-soliton solutions for a generalized Sasa-Satsuma equation. (English) Zbl 1467.35282 Wave Motion 60, 62-72 (2016). MSC: 35Q53 35C08 35Q15 76B15 76D33 78A35 PDFBibTeX XMLCite \textit{X. Geng} and \textit{J. Wu}, Wave Motion 60, 62--72 (2016; Zbl 1467.35282) Full Text: DOI
Wei, Jiao; Geng, Xianguo; Zeng, Xin Quasi-periodic solutions to the hierarchy of four-component Toda lattices. (English) Zbl 1339.37061 J. Geom. Phys. 106, 26-41 (2016). MSC: 37K10 37K60 PDFBibTeX XMLCite \textit{J. Wei} et al., J. Geom. Phys. 106, 26--41 (2016; Zbl 1339.37061) Full Text: DOI
Li, Zhu; Geng, Xianguo; Guan, Liang Algebro-geometric constructions of the Wadati-Konno-Ichikawa flows and applications. (English) Zbl 1337.37055 Math. Methods Appl. Sci. 39, No. 4, 734-743 (2016). MSC: 37K10 14H70 PDFBibTeX XMLCite \textit{Z. Li} et al., Math. Methods Appl. Sci. 39, No. 4, 734--743 (2016; Zbl 1337.37055) Full Text: DOI
Wei, Jiao; Geng, Xianguo A vector generalization of Volterra type differential-difference equations. (English) Zbl 1351.39008 Appl. Math. Lett. 55, 36-41 (2016). MSC: 39A12 15A18 34K06 PDFBibTeX XMLCite \textit{J. Wei} and \textit{X. Geng}, Appl. Math. Lett. 55, 36--41 (2016; Zbl 1351.39008) Full Text: DOI
Wei, Jiao; Geng, Xianguo A hierarchy of new nonlinear evolution equations and generalized bi-Hamiltonian structures. (English) Zbl 1410.35189 Appl. Math. Comput. 268, 664-670 (2015). MSC: 35Q53 35C08 37K10 PDFBibTeX XMLCite \textit{J. Wei} and \textit{X. Geng}, Appl. Math. Comput. 268, 664--670 (2015; Zbl 1410.35189) Full Text: DOI