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.
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