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New mixed solutions generated by velocity resonance in the \((2+1)\)-dimensional Sawada–Kotera equation

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Abstract

Based on the N-soliton solutions of the \((2+1)\)-dimensional Sawada–Kotera equation, the collisions among lump waves, line waves, and breather waves are studied in this paper. By introducing new constraints, the lump wave does not collide with other waves forever, or stays in collision forever. Under the condition of velocity resonance, the soliton molecules consisting of a lump wave, a line wave, and any number of breather waves are derived for the first time. In particular, the interaction of a line wave and a breather wave will generate two breathers under certain conditions, which is worth exploring, and the method can also be extended to other \((2+1)\)-dimensional integrable equations.

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Acknowledgements

This work is supported by National Natural Science Foundation of China under Grant Nos. 12175111 and 11975131, and K.C.Wong Magna Fund in Ningbo University.

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  1. School of Mathematics and Statistics, Ningbo University, Ningbo, 315211, People’s Republic of China

    Zequn Qi, Qingqing Chen, Miaomiao Wang & Biao Li

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  1. Zequn Qi
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  2. Qingqing Chen
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  3. Miaomiao Wang
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  4. Biao Li
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Correspondence to Biao Li.

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Qi, Z., Chen, Q., Wang, M. et al. New mixed solutions generated by velocity resonance in the \((2+1)\)-dimensional Sawada–Kotera equation. Nonlinear Dyn 108, 1617–1626 (2022). https://doi.org/10.1007/s11071-022-07248-2

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