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

A new (2 + 1)-dimensional integrable soliton equation is proposed, which ha s a close connection with the Levi soliton hierarchy. Through the nonlinear ization of the Levi eigenvalue problems, we obtain a finite-dimensional int egrable system. The Abel-Jacobi coordinates are constructed to straighten o ut the Hamiltonian flows, by which the solutions of both the 1 + 1 and 2 1 Levi equations are obtained through linear superpositions. An inversion p rocedure gives the quasi-periodic solution in the original coordinates in t erms of the Riemann theta functions.