Asymptotic multiphase {\(\Sigma\)}-solutions to the singularly perturbed Korteweg-de Vries equation with variable coefficients (Q2255706)

The aim of this paper is to construct the asymptotic solution to the singularly perturbed Korteweg-de Vries equation with variable coefficients. The notion of an asymptotic multiphase \(\Sigma\)-solution is proposed, and an algorithm of its construction in a neighborhood of the point \(t=0\) is given. Some theorems concerning the exactness, with which such local asymptotic solution satisfies the equation under study are proved. The obtained results have a local character.