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Multi-soliton solutions for the two-component modified short pulse equation and its nonlocal reductions via Bäcklund transformations

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Abstract

Using the reciprocal transformation and the associated equation, a Bäcklund transformation (BT) involving both independent and dependent variables is constructed and studied for the two-component modified short pulse (2mSP) equation. Through the permutability property, the related nonlinear superposition formula (NSF) and multi-BT are worked out. The multi-soliton solutions of the 2mSP equation are also constructed by means of multi-BT. By reducing the soliton solutions of the 2mSP equation, multi-soliton solutions for the four \({{\mathcal {P}}}{{\mathcal {T}}}\) symmetric nonlocal reductions, which are the real (complex) reverse space-time nonlocal focusing (defocusing) mSP equations, are calculated respectively. In particular, the multi-cuspon-like solutions and multi-breather-like solutions with the influence of nonlocality as well as their interaction are presented.

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Data Availability Statement

This manuscript has associated data in a data repository [Authors’ comment: All data included in this article are available upon request by contacting the corresponding author.].

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Acknowledgements

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).

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  1. School of Mathematics and Statistics, Nanning Normal University, Nanning, 530001, Guangxi, People’s Republic of China

    Hui Mao

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Mao, H. Multi-soliton solutions for the two-component modified short pulse equation and its nonlocal reductions via Bäcklund transformations. Eur. Phys. J. Plus 138, 769 (2023). https://doi.org/10.1140/epjp/s13360-023-04270-0

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