The Variable Coefcient Modified Kortweg-de Vries Equation And Two-component Nonlinear Schrodinger Equation

In this article, a Variable Coefcient MKdV(VC-MKdV) equation and a two-component Nonlinear Schrodinger equation(2-NLS) are discussed. They are the im-portant models in mathematical physics.First of all, for the VC-MKdV equation, we use the known solutions of the constantcoefcient MKdV equation and the transformation constructed in this paper to get thesolutions of the VC-MKdV equation. Then some interesting graphics are obtained bytaking diferent values of the parameters in solution.Next, the determinant form of the Darboux Transformation(DT) is given for the2-NLS equation. With the help of this form of the DT, some results are obtained asfollows: The picture of the one-fold breather solution(the expression of the solution istoo complicated to write out explicitly); the form, the picture and the track of theone-fold positon solution; the picture and the track of the two-fold positon solutionand the positon-soliton solution.