Two-Phase Solitonlike Solutions of the Cauchy Problem for a Singularly Perturbed Korteweg-De-Vries Equation with Variable Coefficients

Abstract

We describe a set of initial conditions for which the Cauchy problem for a singularly perturbed Korteweg–de-Vries equation with variable coefficients has an asymptotic two-phase solitonlike solution. The notion of the manifold of initial data of the Cauchy problem for which this solution exists is proposed.