Asymptotics of some differential and pseudodifferential equations, and dynamical systems with small dispersion

Asymptotic soliton-type solutions of the Whitham and Boussinesq equations and an asymptotic solution of shock-wave type of the Toda lattice with variable coefficients in the case of small dispersion are constructed. The solutions represent a “distorted” solitary wave (a smoothed shock wave) with amplitude and speed of motion which depend on time, propagating on a smooth “background”.
Bibliography: 27 titles.