Integration of the Korteweg-de Vries equation with time-dependent coefficients in the case of moving eigenvalues of the Sturm–Liouville operator

U.A. Hoitmetov ; T. G. Hasanov

Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2024), pp. 63-78

Résumé

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.

Détail

Keywords: inverse scattering method, Korteweg-de Vries equations, Sturm–Liouville operator.

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