_{Asymptotic solutions to Cauchy problem for Korteweg-de Vries equation with varying coefficients and small parameter}

Abstract:
We consider Cauchy problem for Korteweg-de Vries equation with varying coefficients and small parameter at the higher derivative. Basing on small parameter approach we present algorithm of constructing asymptotical approximation for one phase soliton type solutions to the problem. The theorem on the order with that asymptotical solution satisfies the initial problem is proved.