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Teoreticheskaya i Matematicheskaya Fizika, 2025, Volume 225, Number 1, Pages 177–192
DOI: https://doi.org/10.4213/tmf10960 (Mi tmf10960) 		 
Generalized Darboux transformation and high-order solutions for the modified complex short pulse equation

Hui Mao, Xue Zhang, Fengdie He

School of Mathematics and Statistics, Nanning Normal University, Nanning, Guangxi, China
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DOI: https://doi.org/10.4213/tmf10960
Abstract: We construct the generalized Darboux transformation for the modified complex short pulse (mcSP) equation. As applications, we present high-order solutions for the mcSP equation by the generalized Darboux transformation. In the case of zero seed solution, high-order soliton solutions are derived, and in the case of plane wave seed solution, high-order rogue wave solutions are obtained. As examples, some high-order solutions and their dynamics are illustrated graphically.
Keywords: modified complex short pulse equation, generalized Darboux transformation, high order soliton solutions, high order rogue wave solutions.
Funding agency Grant number
National Natural Science Foundation of China 12261061
Natural Science Foundation of Guangxi Province 2022GXNSFAA035598
This work is supported by the National Natural Science Foundation of China (grant No. 12261061) and the Natural Science Foundation of Guangxi Zhuang Autonomous Region, China (grant No. 2022GXNSFAA035598).
Received: 25.02.2025
Revised: 03.04.2025
Published: 30.09.2025
English version:
Theoretical and Mathematical Physics, 2025, Volume 225, Issue 1, Pages 1844–1858
DOI: https://doi.org/10.1134/S0040577925100101
Document Type: Article
MSC: 37K10;35Q51
Language: Russian
Citation: Hui Mao, Xue Zhang, Fengdie He, “Generalized Darboux transformation and high-order solutions for the modified complex short pulse equation”, TMF, 225:1 (2025), 177–192; Theoret. and Math. Phys., 225:1 (2025), 1844–1858
Citation in format AMSBIB
\Bibitem{MaoZhaHe25}
\by Hui~Mao, Xue~Zhang, Fengdie~He
\paper Generalized Darboux transformation and high-order solutions for the~modified complex short pulse equation
\jour TMF
\yr 2025
\vol 225
\issue 1
\pages 177--192
\mathnet{http://mi.mathnet.ru/tmf10960}
\crossref{https://doi.org/10.4213/tmf10960}
\transl
\jour Theoret. and Math. Phys.
\yr 2025
\vol 225
\issue 1
\pages 1844--1858
\crossref{https://doi.org/10.1134/S0040577925100101}
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