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Soliton and breather solutions of the higher-order modified Korteweg–de Vries equation with constants background

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Abstract

The higher-order modified Korteweg–de Vries (mKdV) equation with constants background is revealed based on the Riemann–Hilbert problem (RHP). With the derivation of RHP, the one-soliton solution (oSS) and simple breather solution (sBS) of the higher-order mKdV equation are obtained for the first time. In addition, the dynamic behavior of the oSS and sBS were further discussed by some corresponding graphs with selecting appropriate parameters, which have not been studied in published works.

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Acknowledgements

The authors are grateful to Prof. S. F. Tian for many valuable discussions.

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  1. School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, 100081, People’s Republic of China

    Jin-Jin Mao, Tian-Zhou Xu & Lin-Fei Shi

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  1. Jin-Jin Mao
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  2. Tian-Zhou Xu
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Mao, JJ., Xu, TZ. & Shi, LF. Soliton and breather solutions of the higher-order modified Korteweg–de Vries equation with constants background. Z. Angew. Math. Phys. 74, 78 (2023). https://doi.org/10.1007/s00033-023-01946-6

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  • DOI: https://doi.org/10.1007/s00033-023-01946-6

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