Geodesic
Integration of the negative order Korteweg-de Vries equation with a self-consistent source in the class of periodic functions
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 32 (2022) no. 2, pp. 228-239

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In this paper, we consider the negative order Korteweg–de Vries equation with a self-consistent integral source. It is shown that the negative-order Korteweg–de Vries equation with a self-consistent integral source 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 negative order Korteweg–de Vries equation with a self-consistent integral source is determined. The obtained results make it possible to apply the inverse problem method to solve the negative order Korteweg–de Vries equation with a self-consistent source in the class of periodic functions.
Keywords: negative-order KdV, self-consistent source, inverse spectral problem. 
@article{VUU_2022_32_2_a4,
     author = {G. U. Urazboev and M. M. Hasanov},
     title = {Integration of the negative order {Korteweg-de} {Vries} equation with a self-consistent source in the class of periodic functions},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {228--239},
     publisher = {mathdoc},
     volume = {32},
     number = {2},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2022_32_2_a4/}
}
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G. U. Urazboev; M. M. Hasanov. Integration of the negative order Korteweg-de Vries equation with a self-consistent source in the class of periodic functions. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 32 (2022) no. 2, pp. 228-239. http://geodesic.mathdoc.fr/item/VUU_2022_32_2_a4/