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.
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 trans- formations 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.
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
关键词
N-孤子解
非线性方程
达布变换
CDGKS方程
相互作用
MKDV方程
单孤子解
矩阵方法
Darboux transformation, (2+1)-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawaka equation,(2+1)-dimensional modified Korteweg-de Vries equation, N-soliton solutions