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

作者：Wang Xin^*; Chen Yong

来源：Communications in Theoretical Physics, 2014, 61(4): 423-430.

DOI：10.1088/0253-6102/61/4/04

• Darboux transformation
• (2 1)-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawaka equation
• (2 1)-dimensional modified Korteweg-de Vries equation
• N-soliton solutions

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.

• 出版日期2014-4-1
• 单位华东师范大学