A (2 + 1)-Dimensional Integrable Breaking Soliton Equation and Its Algebro-Geometric Solutions

Author:

Chen Xiaohong1,Xia Tiecheng2,Zhu Liancheng3

Affiliation:

1. College of Science, Liaoning University of Technology, Jinzhou 121000, China

2. Department of Mathematics, Shanghai University, Shanghai 200444, China

3. School of Electrical Engineering, Liaoning University of Technology, Jinzhou 121000, China

Abstract

A new (2 + 1)-dimensional breaking soliton equation with the help of the nonisospectral Lax pair is presented. It is shown that the compatible solutions of the first two nontrivial equations in the (1 + 1)-dimensional Kaup–Newell soliton hierarchy provide solutions of the new breaking soliton equation. Then, the new breaking soliton equation is decomposed into the systems of solvable ordinary differential equations. Finally, a hyperelliptic Riemann surface and Abel–Jacobi coordinates are introduced to straighten the associated flow, from which the algebro-geometric solutions of the new (2 + 1)-dimensional integrable equation are constructed by means of the Riemann θ functions.

Funder

National Natural Science Foundation of China

Educational Department of Liaoning Province

Publisher

MDPI AG

Reference21 articles.

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