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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». 2022. Vol 41

Exact Traveling Wave Solutions of the Loaded Modified Korteweg-de Vries Equation

Author(s)
Iroda I. Baltaeva1, Ilkham D. Rakhimov1, Muzaffar M. Khasanov1

1Urgench State University, Urgench, Uzbekistan

Abstract
This paper is dedicated to finding the traveling wave solutions of the loaded modified Korteweg-de Vries equation. It is shown to find the solutions via (G’/G) — expansion method which is one of the most effective ways of finding solutions. When the parameters are taken as special values the solitary waves are also derived from the traveling waves. The traveling wave solutions are expressed by the hyperbolic functions, the trigonometric functions and the rational functions. This method is easy to implement using well-known software packages, which allows you to solve complex nonlinear evolution equations of mathematical physics.
About the Authors

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

Ilkham D. Rakhimov, Postgraduate, Urgench State University, Urgench, 220100, Uzbekistan, ilham.rahimov.87@mail.ru

Muzaffar M. Khasanov, Cand. Sci. (Phys.–Math.), Urgench State University, Urgench, 220100, Uzbekistan, mxasanov@mail.ru

For citation
Baltaeva I. I., Rakhimov I. D., Khasanov M. M. Exact Traveling Wave Solutions of the Loaded Modified Korteweg-de Vries Equation. The Bulletin of Irkutsk State University. Series Mathematics, 2022, vol. 41, pp. 85–95. https://doi.org/10.26516/1997-7670.2022.41.85
Keywords
soliton solution, loaded mKdV, nonlinear equations, expansion method
UDC
517.95
MSC
35Q51, 35Q53
DOI
https://doi.org/10.26516/1997-7670.2022.41.85
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