Algebro-geometric solutions to a hierarchy of (1 + 1)-dimensional and two new (2 + 1)-dimensional nonlinear evolution equations

Abstract

Two new 2 + 1 dimensional nonlinear evolution equations are presented. The 2 + 1 dimensional equations closely relate with a hierarchy of 1 + 1 dimensional soliton equations. Through nonlinearizing of Lax pairs, the 1 + 1 dimensional evolution equations are decomposed to the finite dimensional integrable Hamiltonian systems. Finally by applying Riemann–Jacobi inversion technique, the algebro-geometric solutions of the 1 + 1 dimensional soliton equation hierarchy as well as two 2 + 1 dimensional equations are obtained.