UDC 517.9
ASYMPTOTIC STEP-LIKE SOLUTIONS
TO THE KORTEWEG–de VRIES EQUATION WITH VARIABLE
COEFFICIENTS AND A SMALL PARAMETER AT THE HIGHEST DERIVATIVE
Abstract. The paper deals with the Korteweg–de Vries equation with variable coefficients and a small parameter of the first degree at the highest derivative. The notion of an asymptotic solution of a step type is proposed. By means of the non-linear WKB technique, an algorithm for constructing such solutions is proposed and justified. The order, on the small parameter, of the asymptotic accuracy with which the constructed approximate solution satisfies the given equation is established.
Keywords: Korteweg–de Vries equation with variable coefficients, soliton-like solutions, asymptotic solutions, singular pertubation.
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