Algebro-Geometric Solutions of a ($2+1$)-Dimensional Integrable Equation Associated with the Ablowitz-Kaup-Newell-Segur Soliton Hierarchy

Abstract

The ( 2 + 1 )-dimensional Lax integrable equation is decomposed into solvable ordinary differential equations with the help of known ( 1 + 1 )-dimensional soliton equations associated with the Ablowitz-Kaup-Newell-Segur soliton hierarchy. Then, based on the finite-order expansion of the Lax matrix, a hyperelliptic Riemann surface and Abel-Jacobi coordinates are introduced to straighten out the associated flows, from which the algebro-geometric solutions of the ( 2 + 1 )-dimensional integrable equation are proposed by means of the Riemann θ functions.

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

“…Substituting ( 13) into (26), comparing the coefficient of λ2N and λ2N−1 , and considering (18), we can obtain…”

“…In Ref. [18], we have given the algebro-geometric solutions of the known (2 + 1)-dimensional breaking soliton equation associated with the Ablowitz-Kaup-Newell-Segur soliton hierarchy resorting to the direct method.…”