Abstract
The paper deals with constructing the asymptotic solution to the singularly perturbed Korteweg–de Vries equation with variable coefficients. The notion of an asymptotic multiphase Σ-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.
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