The Darboux Transformation And Explicit Solutions Of Soliton Equation Associated With Three Order Matrix Spectral Problem

In this paper the Darboux transformation and explicit solution of a nonlinear evolu-tion equation associate with a3×3matrix spectral problem is studied. First, starting from the known Lax pair of this nonlinear evolution equation, Darboux transformation of this equation is constructed. Then according to the given Darboux transformation, depending on the seed solutions, three explicit expressions of the solutions to the nonlinear evolution equation is obtained and graphics of two solutions are drawn. At last the infinitly many conservation laws of the nonlinear evolution equation is acquired.