Valeriy Samoylenko and Yuliya Samoylenko (National Taras Shevchenko University of Kyiv, Ukraine)

Asymptotic soliton type solutions to singular perturbed Korteweg de Vries equation with variable coefficients

Abstract:
The report deals with a problem of constructing asymptotic solutions to the singularly perturbed Korteweg de Vries equation with variable coefficients.
The algorithms of finding asymptotic one phase and multi phase soliton type solutions are proposed. The statements on justifications of the proposed algorithms are given.
There is also studied the Cauchy problem for the equation mentioned above.