Geodesic
Integration of the mKdV equation with time-dependent coefficients, with an additional term and with an integral source in the class of rapidly decreasing functions
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 34 (2024) no. 2, pp. 248-266

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The work is devoted to the integration of the modified Korteweg–de Vries equation with time-dependent coefficients, an additional term and an integral source in the class of rapidly decreasing functions using the inverse scattering problem method. In this paper, we consider the case when the Dirac operator included in the Lax pairs is not self-adjoint, therefore the eigenvalues of the Dirac operator can be multiples. The evolution of scattering data is obtained for the non-self-adjoint Dirac operator, the potential of which is a solution of the modified Korteweg–de Vries equation with time-dependent coefficients, with an additional term and with an integral source of a class of rapidly decreasing functions. An example is given to illustrate the application of the results obtained.
Keywords: non-self-adjoint Dirac operator, scattering data, Lax pairs
Mots-clés : Jost solutions 
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     author = {U.A. Hoitmetov and Sh. K. Sobirov},
     title = {Integration of the {mKdV} equation with time-dependent coefficients, with an additional term and with an integral source in the class of rapidly decreasing functions},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {248--266},
     publisher = {mathdoc},
     volume = {34},
     number = {2},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2024_34_2_a4/}
}
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U.A. Hoitmetov; Sh. K. Sobirov. Integration of the mKdV equation with time-dependent coefficients, with an additional term and with an integral source in the class of rapidly decreasing functions. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 34 (2024) no. 2, pp. 248-266. http://geodesic.mathdoc.fr/item/VUU_2024_34_2_a4/