Department of Mechanics and Mathematics,

Kyiv Taras Shevchenko National University,

60 Volodymyrska Str.,

01017 Kyiv,

UKRAINE

E-mail: vsam@univ.kiev.ua, yusam@univ.kiev.ua

_{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.