Geodesic
Integration of the negative order Korteweg-de Vries equation with a special source
The Bulletin of Irkutsk State University. Series Mathematics, Tome 44 (2023), pp. 31-43

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In this paper, we consider the negative order Korteweg-de Vries equation with a self-consistent source corresponding to the eigenvalues of the corresponding spectral problem. It is shown that the considered equation can be integrated by the method of the inverse spectral problem. The evolution of the spectral data of the Sturm-Liouville operator with a periodic potential associated with the solution of the considered equation is determined. The results obtained make it possible to apply the inverse problem method for solving the negative order Korteweg-de Vries equation with a self-consistent source corresponding to the eigenvalues of the corresponding spectral problem.
Keywords: negative order Korteweg-de Vries equation, self-consistent source, inverse spectral problem, system of Dubrovin-Trubovitz equations, trace formulas. 
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     author = {Gayrat U. Urazboev and Muzaffar M. Khasanov and Iroda I. Baltaeva},
     title = {Integration of the negative order {Korteweg-de} {Vries} equation with a special source},
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Gayrat U. Urazboev; Muzaffar M. Khasanov; Iroda I. Baltaeva. Integration of the negative order Korteweg-de Vries equation with a special source. The Bulletin of Irkutsk State University. Series Mathematics, Tome 44 (2023), pp. 31-43. http://geodesic.mathdoc.fr/item/IIGUM_2023_44_a2/