Nonlinear differential equations with exact solutions

2003/11/27 by N. A. Kudryashov, Kudryashov, N. A.
Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #nlin.CD #nlin.SI

paper · pdf · doi:10.48550/arxiv.nlin/0311058

28 pages

arxiv created 2003/11/27 · arxiv updated 2009/12/01

Abstract

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 that nonlinear differential equations have exact solution which is general solution of the simplest integrable equation. The Riccati equation is shown to be a building block to find a lot of nonlinear differential equations with exact solutions. Nonlinear differential equations of the second, third and fourth order with special solutions are given. Most of these equations are used at the description of processes in physics and in theory of nonlinear waves.

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