INTEGRATION OF THE NONLINEAR MODIFIED KORTEVEG-DE FRIES EQUATION LOADED IN THE CLASS OF PERIODIC FUNCTIONS

Abstract

A method for solving the Kaup system A number of problems of mathematical physics are reduced to finding the eigenvalues and orthonormalized eigenfunctions of the Sturm-Liouville operator. In particular, when solving the equations of string vibration and heat conduction, which are considered the main equations of classical mathematical physics, by Fourier method, it is necessary to determine the eigenvalues of the Sturm-Liouville boundary value problem, orthonormalized eigenfunctions and expand the arbitrary function into the Fourier series using them.