Geodesic
Integration of negative-order modified Korteweg–de Vries equation with an integral source
Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 63 (2024), pp. 80-90.

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In this paper, it is shown that the modified Korteweg–de Vries (mKdV) equation of negative order with an integral source can be integrated by the method of the inverse spectral problem. The main result of this work is the derivation of the evolution of the spectral data of the Dirac system with a periodic potential associated with the solution of the negative-order modified Korteweg–de Vries equation with an integral source. The obtained results allow us to apply the inverse problem method to solve the negative-order modified Korteweg–de Vries equation with an integral source.
Keywords: modified Korteweg–de Vries equation of negative order, Dirac system, inverse spectral problem, Dubrovin–Trubowitz system of equations, trace formulas 
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G. U. Urazboev; M. M. Khasanov; O. B. Ismoilov. Integration of negative-order modified Korteweg–de Vries equation with an integral source. Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 63 (2024), pp. 80-90. http://geodesic.mathdoc.fr/item/IIMI_2024_63_a5/

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