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The nonlinear partial differential equation is usually very difficult . Exact solution has been some method for solving soliton equations : such as the inverse scattering method , the bilinear method , Darboux transformation method algebraic geometry methods . These methods Darboux transformation method is a powerful tool , it is starting from a trivial solutions of soliton equations to obtain the exact solution of the non-trivial . derived a class associated with it from a 3 × 3 matrix spectral problem nonlinear evolution equations , and use the trace identity that kind of nonlinear evolution equations have the form of generalized Hamilton class of equations in a non-trivial nonlinear evolution equations for its Lax on spectrum issues : auxiliary spectral problem : wherein u, w, v is about x , a function of t , λ is a constant spectrum parameters using Equation TX TU = UT ( 0.4 ) ( U and U addition to u, v, w are replaced u, v, w , have the same form ) is constructed having a multi-parameter Darboux array: Darboux transformation , wherein T ij , 0 , ( i, j = 1,2.3 ) is a function of x and t, and this strict proof . Finally, as an application to the trivial solution u = v = w = 0 as seed solutions obtained by using Darboux transformation of the soliton equations non- trivial exact solution .
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