Integration of the Korteweg-de Vries equation with time-dependent coefficients in the case of moving eigenvalues of the Sturm–Liouville operator
https://doi.org/10.26907/0021-3446-2024-5-63-78
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.
About the Authors
U. A. Hoitmetov
Urgench State University
Uzbekistan
Uzbekistan
Umid Azadovich Hoitmetov
14 H. Alimdjan str., Urgench, 220100
T. G. Khasanov
Urgench State University
Uzbekistan
Uzbekistan
Temur Gafurjonovich Khasanov
14 H. Alimdjan str., Urgench, 220100
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Review
For citations:
Hoitmetov U.A., Khasanov T.G. Integration of the Korteweg-de Vries equation with time-dependent coefficients in the case of moving eigenvalues of the Sturm–Liouville operator. Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika. 2024;(5):63-78. (In Russ.) https://doi.org/10.26907/0021-3446-2024-5-63-78
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