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

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.