Division theorem combined with the Riccati equation for solving some nonlinear Schrödinger-like equations

Abstract

In this paper, division theorem is employed for obtaining the first integral with polynomial coefficients of two-dimensional autonomous planar system, which can construct the periodic and solitary wave solutions of nonlinear partial differential equations by using the solutions of the Riccati equation. The power of this manageable method is presented by applying it to some nonlinear Schrödinger-like equations. This approach can also be applied to other nonlinear differential equations.