Meromorphic solutions of nonlinear ordinary differential equations

Exact solutions of some popular nonlinear ordinary differential equations are analyzed taking their Laurent series into account. Using the Laurent series for solutions of nonlinear ordinary differential equations we discuss the nature of many methods for finding exact solutions. We show that most of these methods are conceptually identical to one another and they allow us to have only the same solutions of nonlinear ordinary differential equations

Soliton Solutions of the Kaup-Kupershmidt and Sawada-Kotera Equations

In this paper I seek soliton solutions of two-component generalizations of the Kaup- Kupershmidt and Sawada-Kotera equations, for this purpose I will apply the extended tanh method. The extended tanh method with a computerized symbolic computation, is used for constructing the travelling wave solutions of coupled nonlinear equations arising in physics. The obtained solutions include soliton, kink and plane periodic solutions. KeyWords: Soliton Solutions; Kaup-Kupershmidt Equation; Sawada-Kotera Equatio

Symbolic computation of solutions for three generalized nonlinear partial differential eQuations by using the tanh method

Three nonlinear partial differential equations, namely, the standard KdV equation, the Boussinesq equation and the generalized fifthorder KdV equation are considered here from of point the view of construct exact solutions for them. The equations that we consider here are in its most general form. New exact solutions which include periodic and soliton solutions are formally derived by using the tanh method. The programming language Matematica is used

Traveling Wave Solutions of ZK-BBM Equation Sine-Cosine Method

Travelling wave solutions are obtained by using a relatively new technique which is called sine-cosine method for ZK-BBM equations. Solution procedure and obtained results re-confirm the efficiency of the proposed scheme

Solving Nonlinear Partial Differential Equations by the sn-ns Method

We present the application of the sn-ns method to solve nonlinear partial differential equations. We show that the well-known tanh-coth method is a particular case of the sn-ns method

Exact Solutions for a Third-Order KdV Equation with Variable Coefficients and Forcing Term

The general projective Riccati equation method and the Exp-function method are used to construct generalized soliton solutions and periodic solutions to special KdV equation with variable coefficients and forcing term

Exact Solitary Wave and Periodic Wave Solutions of a Class of Higher-Order Nonlinear Wave Equations

We study the exact traveling wave solutions of a general fifth-order nonlinear wave equation and a generalized sixth-order KdV equation. We find the solvable lower-order subequations of a general related fourth-order ordinary differential equation involving only even order derivatives and polynomial functions of the dependent variable. It is shown that the exact solitary wave and periodic wave solutions of some high-order nonlinear wave equations can be obtained easily by using this algorithm. As examples, we derive some solitary wave and periodic wave solutions of the Lax equation, the Ito equation, and a general sixth-order KdV equation

Exp-function Method for Wick-type Stochastic Combined KdV-mKdV Equations

Exp-function method is proposed to present soliton and periodic wave solutions for variable coefficients combined KdV- mKdV equation. By means of Hermite transform and white noise analysis, we consider the variable coefficients and Wick-type stochastic combined KdV-mKdV equations. As a result, we can construct new and more general formal solutions. These solutions include exact stochastic soliton and periodic wave solutions.Keywords: combined KdV-mKdV equation, Exp-function method, Wick product, Hermite transform, White noise