Integration of the Korteweg–de Vries Equation with Time-Dependent Coefficients in the Case of Moving Eigenvalues of the Sturm–Liouville Operator

Abstract

The inverse scattering method is used to integrate the Korteweg–de Vries equation with time-dependent coefficients. We derive the evolution of the scattering data of the Sturm–Liouville operator whose coefficient is a solution of the Korteweg–de Vries equation with time-dependent coefficients. An algorithm for constructing exact solutions of the Korteweg–de Vries equation with time-dependent coefficients is also proposed; we reduce it to the inverse problem of scattering theory for the Sturm–Liouville operator. Examples illustrating the stated algorithm are given.

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DOI

10.3103/s1066369x2470035x

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