Darboux Transformations and N-soliton Solutions of Two (2+1)-Dimensional Nonlinear Equations  

作　　者：王鑫 陈勇 

机构地区：[1]Shanghai Key Laboratory of Trustworthy Computing,East China Normal University

出　　处：《Communications in Theoretical Physics》2014年第4期423-430,共8页理论物理通讯（英文版）

基　　金：Supported by the National Natural Science Foundation of China under Grant Nos.11075055,11275072;Innovative Research Team Program of the National Science Foundation of China under Grant No.61021104;National High Technology Research and Development Program under Grant No.2011AA010101;Shanghai Knowledge Service Platform for Trustworthy Internet of Things under Grant No.ZF1213;Talent Fund;K.C.Wong Magna Fund in Ningbo University

摘　　要：Two Darboux transformations of the(2+1)-dimensional Caudrey–Dodd–Gibbon–Kotera–Sawaka(CDGKS)equation and(2+1)-dimensional modified Korteweg-de Vries(mKdV) equation are constructed through the Darboux matrix method, respectively. N-soliton solutions of these two equations are presented by applying the Darboux transformations N times. The right-going bright single-soliton solution and interactions of two and three-soliton overtaking collisions of the(2+1)-dimensional CDGKS equation are studied. By choosing different seed solutions, the right-going bright and left-going dark single-soliton solutions, the interactions of two and three-soliton overtaking collisions, and kink soliton solutions of the(2+1)-dimensional mKdV equation are investigated. The results can be used to illustrate the interactions of water waves in shallow water.

关 键 词：Darboux transformation （2＋1）-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawaka equation （2＋1）-dimensional modified Korteweg-de Vries equation N-soliton solutions 

分 类 号：O415[理学—理论物理]