Zhang, Ning; Xu, Xi-Xiang A family of integrable differential-difference equations: tri-Hamiltonian structure and Lie algebra of vector fields. (English) Zbl 1486.37037 Discrete Dyn. Nat. Soc. 2021, Article ID 9912387, 9 p. (2021). MSC: 37K10 37K60 37K30 35Q51 37J35 PDFBibTeX XMLCite \textit{N. Zhang} and \textit{X.-X. Xu}, Discrete Dyn. Nat. Soc. 2021, Article ID 9912387, 9 p. (2021; Zbl 1486.37037) Full Text: DOI
Xu, Xi-Xiang A family of Liouville integrable lattice equations with a parameter and its two symmetry constraints. (English) Zbl 1274.37039 J. Math. Phys. 53, No. 2, 023519, 16 p. (2012). MSC: 37K10 37K40 37K60 37K15 53D20 PDFBibTeX XMLCite \textit{X.-X. Xu}, J. Math. Phys. 53, No. 2, 023519, 16 p. (2012; Zbl 1274.37039) Full Text: DOI
Li, Yu-Qing; Xu, Xi-Xiang A hierarchy of Liouville integrable lattice equation associated with a three-by-three discrete spectral problem and its infinitely many conservation laws. (English) Zbl 1333.37108 Int. J. Mod. Phys. B 25, No. 18, 2481-2492 (2011). MSC: 37K10 37K05 35Q51 35L60 PDFBibTeX XMLCite \textit{Y.-Q. Li} and \textit{X.-X. Xu}, Int. J. Mod. Phys. B 25, No. 18, 2481--2492 (2011; Zbl 1333.37108) Full Text: DOI
Xu, Xi-Xiang An integrable coupling hierarchy of the MKdV_integrable systems, its Hamiltonian structure and corresponding nonisospectral integrable hierarchy. (English) Zbl 1188.37065 Appl. Math. Comput. 216, No. 1, 344-353 (2010). MSC: 37K10 PDFBibTeX XMLCite \textit{X.-X. Xu}, Appl. Math. Comput. 216, No. 1, 344--353 (2010; Zbl 1188.37065) Full Text: DOI
Ma, Lin-Lin; Xu, Xi-Xiang A family of discrete Hamiltonian equations associated with a discrete three-by-three matrix spectral problem. (English) Zbl 1179.82032 Int. J. Mod. Phys. B 23, No. 19, 3859-3869 (2009). MSC: 82B20 37K60 PDFBibTeX XMLCite \textit{L.-L. Ma} and \textit{X.-X. Xu}, Int. J. Mod. Phys. B 23, No. 19, 3859--3869 (2009; Zbl 1179.82032) Full Text: DOI
Zhao, Qiu-Lan; Xu, Xi-Xiang; Li, Xin-Yue The Liouville integrable systems associated with a new discrete \(3\times 3\) matrix spectral problem. (English) Zbl 1179.39011 Appl. Math. Comput. 215, No. 7, 2557-2564 (2009). MSC: 39A12 37J15 37J35 PDFBibTeX XMLCite \textit{Q.-L. Zhao} et al., Appl. Math. Comput. 215, No. 7, 2557--2564 (2009; Zbl 1179.39011) Full Text: DOI
Xu, Xi-Xiang; Yang, Hong-Xiang A family of discrete integrable coupling systems and its Liouville integrability. (English) Zbl 1230.37088 Mod. Phys. Lett. B 23, No. 13, 1671-1685 (2009). MSC: 37K10 37K30 PDFBibTeX XMLCite \textit{X.-X. Xu} and \textit{H.-X. Yang}, Mod. Phys. Lett. B 23, No. 13, 1671--1685 (2009; Zbl 1230.37088) Full Text: DOI
Li, Xin-Yue; Xu, Xi-Xiang; Zhao, Qiu-Lan The integrable property of Lotka-Volterra type discrete nonlinear lattice soliton systems. (English) Zbl 1156.82332 Mod. Phys. Lett. B 22, No. 21, 2007-2019 (2008). MSC: 82B20 35Q51 35Q53 PDFBibTeX XMLCite \textit{X.-Y. Li} et al., Mod. Phys. Lett. B 22, No. 21, 2007--2019 (2008; Zbl 1156.82332) Full Text: DOI
Xu, Xixiang; Cao, Weili A 2-parameter hierarchy of integrable lattice equations. (English) Zbl 1173.82314 Mod. Phys. Lett. B 22, No. 14, 1389-1400 (2008). MSC: 82B20 35Q51 37L60 PDFBibTeX XMLCite \textit{X. Xu} and \textit{W. Cao}, Mod. Phys. Lett. B 22, No. 14, 1389--1400 (2008; Zbl 1173.82314) Full Text: DOI
Ding, Hai-Yong; Xu, Xi-Xiang; Yang, Hong-Xiang; Tian, Xiang A new hierarchy of discrete integrable model and its Darboux transformation. (English) Zbl 1175.37073 Mod. Phys. Lett. B 21, No. 4, 189-197 (2007). Reviewer: Hu Chuangan (San Jose) MSC: 37K40 37K10 37K15 PDFBibTeX XMLCite \textit{H.-Y. Ding} et al., Mod. Phys. Lett. B 21, No. 4, 189--197 (2007; Zbl 1175.37073) Full Text: DOI
Ding, Hai-Yong; Tian, Xiang; Xu, Xi-Xiang; Yang, Hong-Xiang A hierarchy of discrete integrable system and its coupled enlarged integrable system. (English) Zbl 1178.37098 Mod. Phys. Lett. B 21, No. 2-3, 155-161 (2007). Reviewer: Rakib Efendiev (Baku) MSC: 37K15 37K40 37K60 PDFBibTeX XMLCite \textit{H.-Y. Ding} et al., Mod. Phys. Lett. B 21, No. 2--3, 155--161 (2007; Zbl 1178.37098) Full Text: DOI
Yang, Hongxiang; Xu, Xixiang; Li, Xiuzhen; Li, Changsheng The modified Toda lattice in \((2+1)\)-dimensions and integrable coupling systems. (English) Zbl 1111.37057 Int. J. Mod. Phys. B 20, No. 23, 3341-3355 (2006). MSC: 37K10 37K60 37K15 PDFBibTeX XMLCite \textit{H. Yang} et al., Int. J. Mod. Phys. B 20, No. 23, 3341--3355 (2006; Zbl 1111.37057) Full Text: DOI
Xu, Xixiang; Yang, Hongxiang; Sun, Yepeng Darboux transformation of the modified Toda lattice equation. (English) Zbl 1125.37053 Mod. Phys. Lett. B 20, No. 11, 641-648 (2006). MSC: 37K60 PDFBibTeX XMLCite \textit{X. Xu} et al., Mod. Phys. Lett. B 20, No. 11, 641--648 (2006; Zbl 1125.37053) Full Text: DOI
Sun, Ye-Peng; Chen, Deng-Yuan; Xu, Xi-Xiang Positive and negative hierarchies of nonlinear integrable lattice models and three integrable coupling systems associated with a discrete spectral problem. (English) Zbl 1101.37046 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 64, No. 11, 2604-2618 (2006). MSC: 37K10 37K60 PDFBibTeX XMLCite \textit{Y.-P. Sun} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 64, No. 11, 2604--2618 (2006; Zbl 1101.37046) Full Text: DOI
Yang, Hongxiang; Xu, Xixiang Integrable expanding models for discrete systems application: coupled Toda and relativistic Toda lattice. (English) Zbl 1103.37043 Int. J. Mod. Phys. B 19, No. 13, 2121-2128 (2005). MSC: 37K10 PDFBibTeX XMLCite \textit{H. Yang} and \textit{X. Xu}, Int. J. Mod. Phys. B 19, No. 13, 2121--2128 (2005; Zbl 1103.37043) Full Text: DOI
Yang, Hongxiang; Xu, Xixiang; Ding, Haiyong New hierarchies of integrable positive and negative lattice models and Darboux transformation. (English) Zbl 1081.37040 Chaos Solitons Fractals 26, No. 4, 1091-1103 (2005). Reviewer: Messoud A. Efendiev (Berlin) MSC: 37K10 35A30 35Q51 37K60 PDFBibTeX XMLCite \textit{H. Yang} et al., Chaos Solitons Fractals 26, No. 4, 1091--1103 (2005; Zbl 1081.37040) Full Text: DOI
Xu, Xi-Xiang Factorization of a hierarchy of the lattice soliton equations from a binary Bargmann symmetry constraint. (English) Zbl 1079.37060 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 61, No. 7, 1225-1240 (2005). Reviewer: Messoud A. Efendiev (Berlin) MSC: 37K60 37J35 37K40 37K10 37J10 PDFBibTeX XMLCite \textit{X.-X. Xu}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 61, No. 7, 1225--1240 (2005; Zbl 1079.37060) Full Text: DOI
Yang, Hongxiang; Xu, Xixiang Hamiltonian structure and infinite number of conservation laws for the coupled discrete KdV equations. (English) Zbl 1064.35174 Appl. Math., Ser. B (Engl. Ed.) 19, No. 4, 374-380 (2004). MSC: 35Q53 37K05 PDFBibTeX XMLCite \textit{H. Yang} and \textit{X. Xu}, Appl. Math., Ser. B (Engl. Ed.) 19, No. 4, 374--380 (2004; Zbl 1064.35174) Full Text: DOI
Xu, Xi-xiang A generalized Wadati–Konno–Ichikawa hierarchy and its binary nonlinearization by symmetry constraints. (English) Zbl 1098.37061 Chaos Solitons Fractals 15, No. 3, 475-486 (2003). MSC: 37K10 37J35 PDFBibTeX XMLCite \textit{X.-x. Xu}, Chaos Solitons Fractals 15, No. 3, 475--486 (2003; Zbl 1098.37061) Full Text: DOI