Related papers: Polygons for finding exact solutions of nonlinear …
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…
New method is presented to look for exact solutions of nonlinear differential equations. Two basic ideas are at the heart of our approach. One of them is to use the general solutions of the simplest nonlinear differential equations. Another…
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…
The application of the Kudryashov method for finding exact solutions of the high order nonlinear evolution equations is considered. Some classes of solitary wave solutions for the families of nonlinear evolution equations of fifth, sixth…
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…
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…
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 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…
Direct algebraic method of obtaining exact solutions to nonlinear PDE's is applied to certain set of nonlinear nonlocal evolutionary equations, including nonlinear telegraph equation, hyperbolic generalization of Burgers equation and some…
We propose a new method for constructing exact solutions to nonlinear delay reaction--diffusion equations of the form $$ u_t=ku_{xx}+F(u,w), $$ where $u=u(x,t)$, $w=u(x,t-\tau)$, and $\tau$ is the delay time. The method is based on…
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…
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…
Explicit solutions are obtained for a class of semilinear radial Schrodinger equations with power nonlinearities in multi-dimensions. These solutions include new similarity solutions and other new group-invariant solutions, as well as new…
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…
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…
A general formalism to solve nonlinear differential equations is given. Solutions are found and reduced to those of second order nonlinear differential equations in one variable. The approach is uniformized in the geometry and solves…
Based the homogeneous balance method, a general method is suggested to obtain several kinds of exact solutions for some kinds of nonlinear equations. The validity and reliability of the method are tested by applying it to the Bousseneq…
A symbolic computational algorithm which detects " linear "` solutions of nonlinear polynomial differential equations of single functions, is developed throughout this paper.
This article demonstrates how variation of parameters can be successfully implemented in combination with other classical techniques, such as the method of characteristics, to derive novel classes of solutions to nonlinear partial…
The paper describes a number of simple but quite effective methods for constructing exact solutions of PDEs, that involve a relatively small amount of intermediate calculations. The methods employ two main ideas: (i) simple exact solutions…