New infinite sequence soliton-like solutions of (2+1)-dimensional generalized Calogero-Bogoyavlenskii-Schiff equation

Abstract

This paper will study in detail homogeneous linear ordinary differential equation with constant coefficients of second order and draw new conclusion to construct new infinite sequence soliton-like solutions of high-dimensional nonlinear evolution equations. Step one: the solving of a homogeneous linear ordinary differential equation with constant coefficients of second order is changed into the solving of the quadratic equation with one unknown and the Riccati equation. Based on this, new infinite sequence solutions of homogeneous linear ordinary differential equation with constant coefficients of second order are found by using nonlinear superposition formula for the solutions to Riccati equation. Step two: new infinite sequence soliton-like solutions to (2+1)-dimensional generalized Calogero-Bogoyavlenskii-Schiff equation are constructed using the above conclusion and the symbolic computation system Mathematica.