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«THE BULLETIN OF IRKUTSK STATE UNIVERSITY». SERIES «MATHEMATICS»
«IZVESTIYA IRKUTSKOGO GOSUDARSTVENNOGO UNIVERSITETA». SERIYA «MATEMATIKA»
ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2024. Vol 47

Soliton Solutions of the Negative Order Modified Korteweg – de Vries Equation

Author(s)
Gayrat U. Urazboev1, Iroda I. Baltaeva1, Shoira E. Atanazarova1,2

1Urgench State University, Urgench, Uzbekistan

2Khorezm 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.
About the Authors

Gayrat U. Urazboev, Dr. Sci. (Phys.-Math.), Prof., Urgench State University, Urgench, 220100, Uzbekistan, gayrat71@mail.ru

Iroda I. Baltaeva, Cand. Sci. (Phys.-Math.), Assoc. Prof., Urgench State University, Urgench, 220100, Uzbekistan, iroda-b@mail.ru

Shoira E. Atanazarova, Master (Phys.-Math.), Junior Researcher, Khorezm Branch of V. I. Romanovski Institute of mathematics, Uzbekistan Academy of Science, Urgench, 220100, Uzbekistan, atanazarova94@gmail.com

For citation
Urazboev G. U., Baltaeva I. I., Atanazarova Sh. E. Soliton Solutions of the Negative Order Modified Korteweg – de Vries Equation. The Bulletin of Irkutsk State University. Series Mathematics, 2024, vol. 47, pp. 63–77. https://doi.org/10.26516/1997-7670.2024.47.63
Keywords
negative order modified Korteweg – de Vries equation, soliton, inverse scattering transform, scattering data, potential, reflection coefficient
UDC
517.957
MSC
35P25, 35P30, 35Q51, 35Q53, 37K15
DOI
https://doi.org/10.26516/1997-7670.2024.47.63
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