https://doi.org/10.1140/epjp/s13360-025-06101-w
Regular Article
Integrability and analytic solutions for a damped variable-coefficient fifth-order modified Korteweg-de Vries equation for the surface waves in a strait or large channel
State Key Laboratory of Information Photonics and Optical Communications, Key Laboratory of Mathematics and Information Networks (Ministry of Education) and School of Science, Beijing University of Posts and Telecommunications, 100876, Beijing, China
Received:
4
September
2024
Accepted:
9
February
2025
Published online:
9
April
2025
Investigations on the variable-coefficient nonlinear partial differential equations attract people's attention. In this paper, we investigate a damped variable-coefficient fifth-order modified Korteweg-de Vries equation for some fluids and cosmic plasmas. Under certain variable-coefficient constraints, we find that the equation is Painlevé integrable. By virtue of the real and complex simplified Hirota procedures, multiple real and complex soliton solutions are derived. Via the soliton wave ansatz method, we obtain some other analytic solutions such as the kink, bell, singular and periodic soliton solutions. Moreover, we discuss the influences of variable coefficients in the equation on those solitons graphically.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
