Multi-soliton solutions and long-time asymptotic behavior of the modified Korteweg–de Vries equations

Partial Differential Equations in Applied Mathematics

Jian-Ping Yu¹  Yong-Li Sun² 

[1] Department of Applied Mathematics, University of Science and Technology Beijing, Beijing 100083, PR China;Department of Mathematics, Beijing University of Chemical Technology, Beijing 100029, PR China;

关键词: Modified KdV equation;    Hirota D-operator;    Multi-soliton solution;    Long-time asymptotic behavior;   

DOI  :  

来源: DOAJ

【 摘 要 】

In this paper, two modified KdV (MKdV) equations, one is real and the other is complex, are investigated. By applying the Hirota bilinear operator theory and computer algebra, the corresponding bilinear forms of these two MKdV equations are successfully derived, and then their multi-soliton solutions are obtained and expressed in explicit forms. In order to study the dynamic properties of the obtained multi-soliton solutions, we further analyze their long-time asymptotic behaviors. It follows that the collisions between two solitons are elastic which are graphically shown.

【 授权许可】

Unknown