A METHOD FOR THE ANALITICAL SOLUTIONS OF NONLINEAR EQUATIONS WITH PARTIAL DERIVATIVES AND THE ALGORITM FOR SOLVING THE THIRD-ORDER SPECIAL EQUATION

Abstract

The article considers the problem of the exact analytical solutions finding nonlinear equations of mathematical physics to simulate dynamic systems and nonlinear physical processes. The algorithm of the generalized Fourier method of variables separation for building solutions of nonlinear equations is offered. These equations include linear parts and nonlinear quadratic differential forms consisting of the sum of products of function powers and derivatives. The offered algorithm generates a series of new solutions of third-order partial differential model equations with quadratic nonlinearity.