The Darboux Transformation Of A 3×3 Spectral Problem And The Explicit Solution For Modified Boussinesq Equation

Generally speaking, it is very difficult to get the explicit solutions for nonlinear partial differential equations.However,it is well known that there are many ways to obtain explicit solutions of soliton equations,such as the Inverse Scattering transformation,the Hirota tech-nique,the Darboux transformation ,the algebra-geometric method,and so on.Among the various approaches,Darboux transformation is known to be powerful in finding solutions of soliton equations from a trivial seed.In this paper ,we consider the Modified Boussinesq equation:and its Lax pairs,the spectral problem:and the auxiliary problem:Then,using the equation( U and (U|ˉ) has the same form, except changing y , z into (y|ˉ) , (z|ˉ)),we derived the Darboux matrix with multi-parameters:...