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Uzbekistan Urgench
Year
2024
Volume
34
Issue
2
Pages
248-266
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Section Mathematics
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
Author(-s) Hoitmetov U.A.a, Sobirov Sh.K.a
Affiliations Urgench State Universitya
Abstract 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, Jost solutions, scattering data, Lax pairs
UDC 517.957
MSC 34L25, 35P25, 47A40, 37K15
DOI 10.35634/vm240205
Received 9 April 2024
Language Russian
Citation Hoitmetov U.A., Sobirov Sh.K. 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. Mekhanika. Komp'yuternye Nauki, 2024, vol. 34, issue 2, pp. 248-266.
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