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Dynamics of dark and anti-dark solitons for the x-nonlocal Davey–Stewartson II equation

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Abstract

We investigate the x-nonlocal Davey–Stewartson II equation based on Kadomtsev–Petviashvili hierarchy reduction method, and then report dark solitons and (semi-) rational solutions expressed in the Gram-type determinant. As an application of those obtained analytical solutions, we study the evolution scenarios of the dark/anti-dark solitons on nonzero backgrounds. In addition, we analyze three kinds of the elastic interactions between the dark solitons and/or anti-dark solitons via the asymptotic analysis. In particular, we present the discovery of degenerate two solitons as single dark soliton or single anti-dark soliton. Besides, we investigate five kinds of the four solitons and four kinds of the degenerate four solitons. We find that the degenerate four solitons are different from the general three solitons, since the invisible soliton will still affect the three visible solitons in the interaction region.

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Funding

This work was supported by the National Natural Science Foundation of China (Grant No. 11975172).

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Authors and Affiliations

  1. Research Center of Nonlinear Science, School of Mathematical and Physical Sciences, Wuhan Textile University, Wuhan, 430200, China

    Cui-Cui Ding, Qin Zhou & Yunzhou Sun

  2. Radiation Physics Laboratory, Department of Physics, Faculty of Sciences, Badji Mokhtar University, P. O. Box 12, 23000, Annaba, Algeria

    Houria Triki

  3. Department of Mathematics and Physics, Grambling State University, Grambling, LA, 71245, USA

    Anjan Biswas

  4. Mathematical Modeling and Applied Computation (MMAC) Research Group, Department of Mathematics, King Abdulaziz University, Jidda, 21589, Saudi Arabia

    Anjan Biswas

  5. Department of Applied Mathematics, National Research Nuclear University, 31 Kashirskoe Hwy, Moscow, 115409, Russian Federation

    Anjan Biswas

  6. Department of Applied Sciences, Cross-Border Faculty, Dunarea de Jos University of Galati, 111 Domneasca Street, Galati-800201, Romania

    Anjan Biswas

  7. Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Medunsa-0204, South Africa

    Anjan Biswas

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  1. Cui-Cui Ding
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Ding, CC., Zhou, Q., Triki, H. et al. Dynamics of dark and anti-dark solitons for the x-nonlocal Davey–Stewartson II equation. Nonlinear Dyn 111, 2621–2629 (2023). https://doi.org/10.1007/s11071-022-07938-x

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