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Integro-differential equations and functional analysis
Soliton solutions of the negative order modified Korteweg – de Vries equation
Gayrat U. Urazboeva, Iroda I. Baltaevaa, Shoira E. Atanazarovaab a Urgench State University, Urgench, Uzbekistan
b Khorezm branch of V. I. Romanovski Institute of Mathematics, Uzbekistan Academy of Science, Urgench, Uzbekistan
Abstract:
In this paper, we study the negative order modified Korteweg-de Vries (nmKdV) equation in the class of rapidly decreasing functions. In particular, we show that the inverse scattering transform technique can be applied to obtain the time dependence of scattering data of the operator Dirac with potential being the solution of the considered problem. We demonstrate the explicit representation of one soliton solution of nmKdV based on the obtained results.
Keywords:
negative order modified Korteweg – de Vries equation, soliton, inverse scattering transform, scattering data, potential, reflection coefficient.
Received: 22.06.2023 Revised: 19.10.2023 Accepted: 21.11.2023
Citation:
Gayrat U. Urazboev, Iroda I. Baltaeva, Shoira E. Atanazarova, “Soliton solutions of the negative order modified Korteweg – de Vries equation”, Bulletin of Irkutsk State University. Series Mathematics, 47 (2024), 63–77
Linking options:
https://www.mathnet.ru/eng/iigum555 https://www.mathnet.ru/eng/iigum/v47/p63
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Abstract page: | 62 | Full-text PDF : | 49 | References: | 8 |
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