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

Xiaohong Chen (), Tiecheng Xia and Liancheng Zhu
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Xiaohong Chen: College of Science, Liaoning University of Technology, Jinzhou 121000, China
Tiecheng Xia: Department of Mathematics, Shanghai University, Shanghai 200444, China
Liancheng Zhu: School of Electrical Engineering, Liaoning University of Technology, Jinzhou 121000, China

Mathematics, 2024, vol. 12, issue 13, 1-11

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.

Keywords: breaking soliton equation; algebro-geometric solution; Abel–Jacobi coordinates; Riemann ? function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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