Quasi-periodic solution of a new (2+1)-dimensional coupled soliton equation

Abstract

A new (2+1)-dimensional integrable soliton equation is proposed, which has a close connection with the Levi soliton hierarchy. Through the nonlinearization of the Levi eigenvalue problems, we obtain a finite-dimensional integrable system. The Abel-Jacobi coordinates are constructed to straighten out the Hamiltonian flows, by which the solutions of both the 1 + 1 and 2 + 1 Levi equations are obtained through linear superpositions. An inversion procedure gives the quasi-periodic solution in the original coordinates in terms of the Riemann theta functions.