Nonlinear Second Order Ode's: Factorizations and Particular Solutions

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.

Solitary wave solutions of selective nonlinear diffusion-reaction equations using homogeneous balance method

“…Note that for D = 1, and for certain choices of the parameters in eq. (4), the factorization method is employed [21] and exponential solutions are obtained.…”

“…In recent years, various direct methods were proposed to find exact solutions of nonlinear partial differential equations (NLPDEs) in general. These methods include, Bäcklund transformation (BT) [5], (G /G)-expansion method [6,7], auxiliary equation method [8][9][10][11][12], exponential function method [13,14], homogeneous balance (HB) method [15][16][17], variational iteration method [18][19][20], factorization method [21], algebraic method [22] and Weiss approach [23]. Whereas some of these methods are of general nature in the sense that they can be employed to any NLPDE, others are equation-specific.…”

The classification of single travelling wave solutions to the Camassa–Holm–Degasperis–Procesi equation for some values of the convective parameter

“…Furthermore, Wang and Li [8] used Liu's method and factorization method proposed by Cornejo-Pérez and Rosu [9][10][11] to give single solitary and multi-solitary solutions to some nonlinear differential equations. Yang [12] studied the classification of envelope solutions to SD equation by Liu's method.…”

An irrational trial equation method and its applications

“…[5] and references therein). Based on the decomposition of differential operator, an interesting and powerful approach, namely factorization method [6][7][8] has been introduced to deal with nonlinear differential equations. Recently, in a series of papers [9][10][11][12], Liu proposed the trial equation method which is different from those direct methods.…”