Nonlinear second order ODE's: Factorizations and particular solutions

TL;DR

This paper develops an extended factorization method to find particular solutions for several nonlinear second order differential equations, including modified Emden, generalized Lienard, convective Fisher, and generalized Burgers-Huxley, some in the travelling frame.

Contribution

It introduces an extended factorization technique for solving complex nonlinear second order ODEs, providing new particular solutions for several important equations.

Findings

Derived particular solutions for modified Emden, generalized Lienard, convective Fisher, and generalized Burgers-Huxley equations.

Extended a previous factorization method to handle more complex nonlinear equations.

Solutions obtained in the travelling frame for certain equations.

Abstract

We present particular solutions for the following important nonlinear second order differential equations: modified Emden, generalized Lienard, convective Fisher, and generalized Burgers-Huxley. For the latter two equations these solutions are obtained in the travelling frame. All these particular solutions are the result of extending a simple and efficient factorization method that we developed in Phys. Rev. E 71 (2005) 046607