Asymptotic Multiphase Solitonlike Solutions of the Cauchy Problem for a Singularly Perturbed Korteweg–de-Vries Equation with Variable Coefficients

Abstract

We describe the set of initial conditions under which the Cauchy problem for a singularly perturbed Korteweg–de-Vries equation with variable coefficients has an asymptotic multiphase solitonlike solution. The notion of manifold of initial values for which the above-mentioned solution exists is proposed for the analyzed Cauchy problem. The statements on the estimation of the difference between the exact and constructed asymptotic solutions are proved for the Cauchy problem.