Asymptotic solutions of soliton type of the Korteweg–de Vries equation with variable coefficients and singular perturbation
The paper deals with the singularly perturbed Korteweg–de Vries equation with variable coefficients. The equation describes wave processes in various inhomogeneous media with variable characteristics and small dispersion. We consider the general algorithm of construction of asymptotic solutions of soliton type to the equation and present its approximate solutions of this type. We analyze properties of the constructed asymptotic solution depending on a small parameter. The results are demonstrated by the examples of the studied equation. We show that for an adequate description of quali