Existence and Multiplicity of Solutions for a Class of Nonlinear Schrodinger- KdV Equations

Abstract

In this paper, a class of coupled Riccati equations by using some special solutions of nonlinear coupled Schrod- inger-KdV equations of a number of exact analytical group, obtain the precise solution and two groups of new solitary wave solutions of the equations and several general forms. With the help of computer symbolic computation technology, using F- expansion method to obtain exact solutions of the coupled Schrodinger-KdV equations, including the trigonomet- ric function solutions, hyperbolic function solutions and Jacobian elliptic function solutions, the precise solution is widely used in plasma physics. In the past few decades, many scholars on the nonlinear Schrodinger equation and the existence of solutions of multi solution problem is studied, and the nonlinear term of the proposed restriction conditions become more and more weak. This paper firstly studies the ground state spectra with zero point solutions of Schrodinger equation. When the nonlinearity is superlinear, we give a more direct, simple and convenient method.