Asymptotic solutions of the Cauchy problem for the singularly perturbed Korteweg-de Vries equation with variable coefficients

We propose an algorithm for the construction of an asymptotic solution of the Cauchy problem for the singularly perturbed Korteweg-de Vries equation with variable coefficients and prove a theorem on the estimation of its precision. __________ Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 1, pp. 122–132, January, 2007.