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integrable discretization of soliton equations via bilinear method and Backlund transformation

Science China Mathematics 2015年第2期58卷 279-296页

作者： ZHANG Ying Nan CHANG Xiang Ke HU Juan HU Xing Biao TAM Hon-Wah Institute of Computational Mathematics and Scientific Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences School of Mathematical Sciences University of Chinese Academy of Sciences Department of Applied Mathematics Zhejiang University of Technology Department of Computer Science Hong Kong Baptist University

We present a systematic procedure to derive discrete analogues of integrable PDEs via Hirota’s bilinear *** approach is mainly based on the compatibility between an integrable system and its B¨acklund *** apply this procedure to several equations,including the extended Korteweg-deVries(Kd V)equation,the extended Kadomtsev-Petviashvili(KP)equation,the extended Boussinesq equation,the extended Sawada-Kotera(SK)equation and the extended Ito equation,and obtain their associated semidiscrete *** the continuum limit,these differential-difference systems converge to their corresponding smooth *** these new integrable systems,their B¨acklund transformations and Lax pairs are derived.

关键词： integrable discretization bilinear method Backlund transformation

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Multi-Soliton Solutions and integrable discretization for a Coupled Modified Volterra Lattice Equation

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Communications in Theoretical Physics 2012年第8期58卷 244-250页

作者：赵海琼朱佐农 Business Information Management School Shanghai Institute of Foreign Trade Department of Mathematics Shanghai Jiao Tong University

In this paper, we study a coupled modified Volterra lattice equation which is an integrable semidiscrete version of the coupled KdV and the coupled mKdV equation. By using the Darboux transformation, we obtain its new explicit solutions including multi-soliton and multi-positon. Furthermore, an integrable discretization of the coupled modified Volterra lattice equation is constructed.

关键词： coupled modified Volterra lattice multi-soliton integrable discretization

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integrable discretizations of the Dym equation

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Frontiers of Mathematics in China 2013年第5期8卷 1017-1029页

作者： Bao-Feng FENG Jun-ichi INOGUCHI Kenji KAJIWARA Ken-ichi MARUNO Yasuhiro OHTA Department of Mathematics The University of Texas-Pan American Edinburg TX 78539 USA Department of Mathematical Sciences Yamagata University 1-4-12 Kojirakawa-machi Yamagata 990-8560 Japan Institute of Mathematics for Industry Kyushu University 744 Motooka Fukuoka 819-8581 Japan Department of Mathematics Kobe University Rokko Kobe 657-8501 Japan

integrable discretizations of are proposed. N-soliton solutions for analogues of the complex and real Dym the complex and real Dym equations both semi-discrete and fully discrete equations are also presented.

关键词： Dym equation integrable discretization N-soliton solution

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