New complex soliton-like solutions of combined KdV equation with variable coefficients and forced term

Abstract

The [G()]/[G()] expansion method is extensively studied to search for new infinite sequence of complex solutions to nonlinear evolution equations with variable coefficients. According to a function transformation, the solving of homogeneous linear ordinary differential equation with constant coefficients of second order can be changed into the solving of a one-unknown quadratic equation and the Riccati equation. Based on this, new infinite sequence complex solutions of homogeneous linear ordinary differential equation with constant coefficients of second order are obtained by the nonlinear superposition formula of the solutions to Riccati equation. By means of the new complex solutions, new infinite sequence complex soliton-like exact solutions to the combined KdV equation with variable coefficients and forced term are constructed with the help of symbolic computation system Mathematica.