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Riemann–Hilbert approach for a (2+1) dimensional Kundu–Mukherjee–Naskar equation

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Abstract

This paper concentrates on a (2+1) dimensional Kundu–Mukherjee–Naskar (KMN) equation. The (2+1) dimensional KMN equation was decomposed into two (1+1)-dimensional nonlinear evolution equations, resulting in the emergence of three spectral matrices. From these three spectral matrices, the Riemann–Hilbert problem of the (2+1) dimensional KMN equation is constructed. By solving the Riemann–Hilbert problem in the case that the jump matrix is identity matrix, that is, when the scattering data \(s_{12}(\lambda )\) and \(s_{21}(\lambda )\) are 0, the multi-soliton solutions for the (2+1) dimensional KMN equation are acquired. In particular, the one-soliton solution, two-soliton solution and three-soliton solution of the (2+1) dimensional KMN equation are given in detail. Substituting these solutions into Eq. (2) reveals that they satisfied Eq. (2) and are analyzed graphically. It can be seen from the picture that when \(\lambda \) is purely imaginary, the interaction between solitons is periodic.

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The authors declare that all data supporting the findings of this study are available within the article.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China under (Grant No. 12361052), the Natural Science Foundation of Inner Mongolia Autonomous Region, China under (Grant Nos. 2020LH01010, 2022ZD05), Program for Innovative Research Team in Universities of Inner Mongolia Autonomous Region (Grant No. NMGIRT2414), the Fundamental Research Funds for the Inner Mongolia Normal University (Grant Nos. 2022JBTD007, 2022JBXC013), and Graduate Students Research & Innovation Fund of Inner Mongolia Autonomous Region (Grant No. B20231053Z). The Key Laboratory of Infinite-dimensional Hamiltonian System and Its Algorithm Application (Inner Mongolia Normal University), Ministry of Education (2023KFZR01, 2023KFZR02).

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Authors and Affiliations

  1. College of Mathematics Science, Inner Mongolia Normal University, Hohhot, 010022, People’s Republic of China

    Dan Zhao &  Zhaqilao

  2. Center for Applied Mathematical Science, Hohhot, 010022, Inner Mongolia, People’s Republic of China

    Dan Zhao &  Zhaqilao

  3. Laboratory of Infinite-dimensional Hamiltonian System and Its Algorithm Application, Ministry of Education (IMNU), Hohhot, 010022, People’s Republic of China

    Dan Zhao &  Zhaqilao

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  1. Dan Zhao
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Zhao, D., Zhaqilao Riemann–Hilbert approach for a (2+1) dimensional Kundu–Mukherjee–Naskar equation. Nonlinear Dyn (2024). https://doi.org/10.1007/s11071-024-09668-8

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