The Explicit Solutions Of Two Nonlinear Evolution Equations

In this thesis, the explicit solutions of two nonlinear evolution equations are obtained. First, a new coupled nonlinear Schrodinger type equation is proposed, and then its Lax pair is derived. Based on the gauge transformation between the spetral problems, a Darboux Transformation is structured, by which some explicit solutions of the coupled nonlinear Schrodinger type equation are obtained, including rational and periodic solutions. Second, a (3+1)-dimensional KdV equation is considered, by introducing logarithmic transformation, and using bilinear derivation method, N-soliton solution and Wronskian solution of the equation have been obtained.