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CONTENTSIntroductionChapter I. The Korteweg-de Vries equation with variable coefficients § 1. Basic definitions. A single-phase soliton-form solution of the Korteweg-de Vries equation with variable… (More)
We present a new method for studying the interaction of solitons for non-integrable Korteweg-de Vries (KdV) type equations with small disper- sion and test this method for the KdV equation.
We consider a class of semi-linear wave equations with a small parameter and nonlinearities which provide the equations having exact kink-type solutions. We declare sufficient conditions for the… (More)
A justification is given of the asymptotic solution of phase-field equations, which lead to a modified Stefan problem. Solubility of the modified Stefan problem and of the phase-field equations is… (More)
A technique is developed in this work to construct asymptotic solutions describing the resonant interaction of shortwaves in weakly nonlinear dispersive media. Also included is the process of… (More)
Abstract In this paper we consider equations of an isentropic viscous gas when the Reynolds number is large. In a three-dimensional domain with an arbitrary smooth boundary we construct an asymptotic… (More)