相关论文: Simplest equation method to look for exact solutio…

New method for finding exact solutions of nonlinear differential equations is presented. It is based on constructing the polygon corresponding to the equation studied. The algorithms of power geometry are used. The method is applied for…

The modification of simplest equation method to look for exact solutions of nonlinear partial differential equations is presented. Using this method we obtain exact solutions of generalized Korteweg-de Vries equation with cubic source and…

New problem is considered that is to find nonlinear differential equations with special solutions. Method is presented to construct nonlinear ordinary differential equations with exact solution. Crucial step to the method is the assumption…

A method for finding exact solutions of nonlinear differential equations is presented. Our method is based on the application of the Newton polygons corresponding to nonlinear differential equations. It allows one to express exact solutions…

One of old methods for finding exact solutions of nonlinear differential equations is considered. Modifications of the method are discussed. Application of the method is illustrated for finding exact solutions of the Fisher equation and…

We analyze the common errors of the recent papers in which the solitary wave solutions of nonlinear differential equations are presented. Seven common errors are formulated and classified. These errors are illustrated by using multiple…

New problem is studied that is to find nonlinear differential equations with special solutions expressed via the Weierstrass function. Method is discussed to construct nonlinear ordinary differential equations with exact solutions. Main…

Often a non-linear mechanical problem is formulated as a non-linear differential equation. A new method is introduced to find out new solutions of non-linear differential equations if one of the solutions of a given non-linear differential…

We discuss a new version of a method for obtaining exact solutions of nonlinear partial differential equations. We call this method the Simple Equations Method (SEsM). The method is based on representation of the searched solution as…

In order to find closed form solutions of nonintegrable nonlinear ordinary differential equations, numerous tricks have been proposed. The goal of this short review is to recall classical, 19th-century results, completed in 2006 by…

We present a short review of the evolution of the methodology of the Method of simplest equation for obtaining exact particular solutions of nonlinear partial differential equations (NPDEs) and the recent extension of a version of this…

This article proposes a novel approach for determining exact solutions to nonlinear ordinary differential equations. The recommended iterative method provides the solution via a rapidly converging series that readily approaches a closed…

Our goal is to find closed form analytic expressions for the solitary waves of nonlinear nonintegrable partial differential equations. The suitable methods, which can only be nonperturbative, are classified in two classes. In the first…

The concept of quasi-exact solutions of nonlinear differential equations is introduced. Quasi-exact solution expands the idea of exact solution for additional values of parameters of differential equation. These solutions are approximate…

New approach is presented to search exact solutions of nonlinear differential equations. This method is used to look for exact solutions of the Korteveg -- de Vries -- Burgers equation. New exact solitary waves of the Korteveg -- de Vries…

We discuss the application of a variant of the method of simplest equation for obtaining exact traveling wave solutions of a class of nonlinear partial differential equations containing polynomial nonlinearities. As simplest equation we use…

This chapter is mainly a tutorial introduction to methods recently developed in order to find all (as opposed to some) meromorphic particular solutions of given nonintegrable, autonomous, algebraic ordinary differential equations of any…

We apply the method of simplest equation for obtaining exact solitary traveling-wave solutions of nonlinear partial differential equations that contain monomials of odd and even grade with respect to participating derivatives. We consider…

The method of simplest equation is applied for obtaining exact solitary traveling-wave solutions of nonlinear partial differential equations that contain monomials of odd and even grade with respect to participating derivatives. The used…

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…