Li, Jian; Xia, Tiecheng Long-time asymptotics to the defocusing generalized nonlinear Schrödinger equation with the decaying initial value problem. (English) Zbl 07816025 Math. Methods Appl. Sci. 46, No. 18, 18706-18728 (2023). MSC: 35Q51 35Q15 37K10 PDFBibTeX XMLCite \textit{J. Li} and \textit{T. Xia}, Math. Methods Appl. Sci. 46, No. 18, 18706--18728 (2023; Zbl 07816025) Full Text: DOI
Yang, Yingmin; Xia, Tiecheng; Liu, Tongshuai Darboux transformation and exact solution to the nonlocal Kundu-Eckhaus equation. (English) Zbl 1514.35419 Appl. Math. Lett. 141, Article ID 108602, 7 p. (2023). MSC: 35Q55 35C08 37K35 35Q15 37K10 PDFBibTeX XMLCite \textit{Y. Yang} et al., Appl. Math. Lett. 141, Article ID 108602, 7 p. (2023; Zbl 1514.35419) Full Text: DOI
Kang, Zhou-Zheng; Xia, Tie-Cheng; Ma, Wen-Xiu Riemann-Hilbert method for multi-soliton solutions of a fifth-order nonlinear Schrödinger equation. (English) Zbl 1458.35388 Anal. Math. Phys. 11, No. 1, Paper No. 14, 13 p. (2021). MSC: 35Q55 35Q15 37K10 35C08 82D40 PDFBibTeX XMLCite \textit{Z.-Z. Kang} et al., Anal. Math. Phys. 11, No. 1, Paper No. 14, 13 p. (2021; Zbl 1458.35388) Full Text: DOI
Wei, Hanyu; Xia, Tiecheng Constructing super D-Kaup-Newell hierarchy and its nonlinear integrable coupling with self-consistent sources. (English) Zbl 1441.37075 Front. Math. China 14, No. 6, 1353-1366 (2019). MSC: 37K10 35Q53 PDFBibTeX XMLCite \textit{H. Wei} and \textit{T. Xia}, Front. Math. China 14, No. 6, 1353--1366 (2019; Zbl 1441.37075) Full Text: DOI
Hu, Beibei; Xia, Tiecheng; Zhang, Ning The unified transform method to initial-boundary value problem for a coupled cubic-quintic nonlinear Schrödinger system. (English) Zbl 1428.35517 Complex Anal. Oper. Theory 13, No. 3, 1143-1159 (2019). MSC: 35Q55 37K10 35Q51 35Q15 78A60 PDFBibTeX XMLCite \textit{B. Hu} et al., Complex Anal. Oper. Theory 13, No. 3, 1143--1159 (2019; Zbl 1428.35517) Full Text: DOI
Kang, Zhou-Zheng; Xia, Tie-Cheng; Ma, Wen-Xiu Riemann-Hilbert approach and \(N\)-soliton solution for an eighth-order nonlinear Schrödinger equation in an optical fiber. (English) Zbl 1459.35303 Adv. Difference Equ. 2019, Paper No. 188, 14 p. (2019). MSC: 35Q15 35Q55 37K10 35C08 PDFBibTeX XMLCite \textit{Z.-Z. Kang} et al., Adv. Difference Equ. 2019, Paper No. 188, 14 p. (2019; Zbl 1459.35303) Full Text: DOI arXiv
Wei, Hanyu; Xia, Tiecheng A integrable generalized super-NLS-mKdV hierarchy, its self-consistent sources, and conservation laws. (English) Zbl 1406.35373 Adv. Math. Phys. 2018, Article ID 1396794, 9 p. (2018). MSC: 35Q55 35Q53 17A70 37K10 PDFBibTeX XMLCite \textit{H. Wei} and \textit{T. Xia}, Adv. Math. Phys. 2018, Article ID 1396794, 9 p. (2018; Zbl 1406.35373) Full Text: DOI
Hu, Beibei; Xia, Tiecheng A Fokas approach to the coupled modified nonlinear Schrödinger equation on the half-line. (English) Zbl 1397.35274 Math. Methods Appl. Sci. 41, No. 13, 5112-5123 (2018). MSC: 35Q55 35Q51 35Q15 37K10 37K15 78A60 45D05 45C05 35P15 PDFBibTeX XMLCite \textit{B. Hu} and \textit{T. Xia}, Math. Methods Appl. Sci. 41, No. 13, 5112--5123 (2018; Zbl 1397.35274) Full Text: DOI
Wei, Hanyu; Xia, Tiecheng Nonlinear bi-integrable couplings of Broer-Kaup-Kupershmidt hierarchy with self-consistent sources. (Chinese. English summary) Zbl 1389.35270 Appl. Math., Ser. A (Chin. Ed.) 32, No. 2, 165-175 (2017). MSC: 35Q51 37K10 37K40 PDFBibTeX XMLCite \textit{H. Wei} and \textit{T. Xia}, Appl. Math., Ser. A (Chin. Ed.) 32, No. 2, 165--175 (2017; Zbl 1389.35270)
Li, Qian; Xia, Tiecheng; Yue, Chao Algebro-geometric solutions for the generalized nonlinear Schrödinger hierarchy. (English) Zbl 1326.37043 J. Nonlinear Sci. Appl. 9, No. 2, 661-676 (2016). MSC: 37K10 35Q35 37K20 PDFBibTeX XMLCite \textit{Q. Li} et al., J. Nonlinear Sci. Appl. 9, No. 2, 661--676 (2016; Zbl 1326.37043) Full Text: DOI Link
Wei, Hanyu; Xia, Tiecheng A new Lie algebra structure, new nonlinear integrable couplings and their Hamiltonian structures. (English) Zbl 1313.35282 Chin. J. Eng. Math. 31, No. 3, 463-474 (2014). MSC: 35Q51 37K40 37K10 37K05 PDFBibTeX XMLCite \textit{H. Wei} and \textit{T. Xia}, Chin. J. Eng. Math. 31, No. 3, 463--474 (2014; Zbl 1313.35282) Full Text: DOI
Wei, Hanyu; Xia, Tiecheng; Yue, Chao Nonlinear integrable couplings of the super Broer-Kaup-Kupershmidt hierarchy and its Hamiltonian structures. (Chinese. English summary) Zbl 1299.35256 Acta Math. Sci., Ser. A, Chin. Ed. 33, No. 4, 686-695 (2013). MSC: 35Q51 37K40 37J35 PDFBibTeX XMLCite \textit{H. Wei} et al., Acta Math. Sci., Ser. A, Chin. Ed. 33, No. 4, 686--695 (2013; Zbl 1299.35256)
Wang, Hui; Xia, Tie-cheng Three nonlinear integrable couplings of the nonlinear Schrödinger equations. (English) Zbl 1225.37076 Commun. Nonlinear Sci. Numer. Simul. 16, No. 11, 4232-4237 (2011). MSC: 37K10 35Q55 37K30 PDFBibTeX XMLCite \textit{H. Wang} and \textit{T.-c. Xia}, Commun. Nonlinear Sci. Numer. Simul. 16, No. 11, 4232--4237 (2011; Zbl 1225.37076) Full Text: DOI
You, Fucai; Xia, Tiecheng; Zhang, Jiao Frobenius integrable decompositions for two classes of nonlinear evolution equations with variable coefficients. (English) Zbl 1185.37151 Mod. Phys. Lett. B 23, No. 12, 1519-1524 (2009). Reviewer: M. Marin (Brasov) MSC: 37K10 35Q51 37K35 35Q53 35G25 PDFBibTeX XMLCite \textit{F. You} et al., Mod. Phys. Lett. B 23, No. 12, 1519--1524 (2009; Zbl 1185.37151) Full Text: DOI
Xia, Tiecheng; Jiao, Zhang; You, Fucai A new loop algebra and its application to the multi-component S-mKdV hierarchy. (English) Zbl 1130.37034 Chaos Solitons Fractals 33, No. 3, 870-878 (2007). MSC: 37K30 37K10 37K15 PDFBibTeX XMLCite \textit{T. Xia} et al., Chaos Solitons Fractals 33, No. 3, 870--878 (2007; Zbl 1130.37034) Full Text: DOI
Zhoa, Wenying; Xia, Tiecheng The multi-component NLS-mKdV hierarchy and its integrable couplings system. (English) Zbl 1129.35448 Far East J. Dyn. Syst. 8, No. 1, 105-113 (2006). MSC: 35Q51 37K10 37K30 35Q55 PDFBibTeX XMLCite \textit{W. Zhoa} and \textit{T. Xia}, Far East J. Dyn. Syst. 8, No. 1, 105--113 (2006; Zbl 1129.35448)
Yu, Fajun; Xia, Tiecheng; Zhang, Hongqing The multi-component TD hierarchy and its multi-component integrable coupling system with five arbitrary functions. (English) Zbl 1102.37044 Chaos Solitons Fractals 27, No. 4, 1036-1041 (2006). MSC: 37K10 37K30 35Q58 PDFBibTeX XMLCite \textit{F. Yu} et al., Chaos Solitons Fractals 27, No. 4, 1036--1041 (2006; Zbl 1102.37044) Full Text: DOI
Xia, Tie-Cheng; Yu, Fa-Jun; Chen, Deng-Yuan The multi-component Yang hierarchy and its multi-component integrable coupling system with two arbitrary functions. (English) Zbl 1064.37056 Chaos Solitons Fractals 24, No. 1, 235-240 (2005). MSC: 37K10 PDFBibTeX XMLCite \textit{T.-C. Xia} et al., Chaos Solitons Fractals 24, No. 1, 235--240 (2005; Zbl 1064.37056) Full Text: DOI
Xia, Tiecheng; Yu, Fajun; Chen, Dengyuan The multi-component generalized Wadati-Konono-Ichikawa (WKI) hierarchy and its multi-component integrable couplings system with two arbitrary functions. (English) Zbl 1088.37038 Chaos Solitons Fractals 24, No. 3, 877-883 (2005). MSC: 37K10 35Q58 35Q51 PDFBibTeX XMLCite \textit{T. Xia} et al., Chaos Solitons Fractals 24, No. 3, 877--883 (2005; Zbl 1088.37038) Full Text: DOI
Xia, Tiecheng; Chen, Xiaohong; Chen, Dengyuan A Lax integrable hierarchy, bi-Hamiltonian structure and finite-dimensional Liouville integrable involutive systems. (English) Zbl 1060.37062 Chaos Solitons Fractals 22, No. 4, 939-945 (2004). MSC: 37K10 35Q55 35Q53 PDFBibTeX XMLCite \textit{T. Xia} et al., Chaos Solitons Fractals 22, No. 4, 939--945 (2004; Zbl 1060.37062) Full Text: DOI