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Soliton, breather-like and dark-soliton-breather-like solutions for the coupled long-wave–short-wave system

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Abstract

In this paper, we will obtain the exact N-soliton solution of the coupled long-wave–short-wave system via the developed Hirota bilinear method. Through manipulating the relevant parameters, we will construct different types of solutions which include breather-like solutions and dark-soliton-breather-like solutions. Moreover, we will demonstrate that the interactions of two-soliton and two-breather-like solutions are all elastic through asymptotic analysis method. Finally, we will display the interactions through illustrations.

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Data availability

The datasets generated during or analyzed during the current study are available from the corresponding author on reasonable request.

References

  1. Ablowitz, M.J., Segur, H.: On the evolution of packets of water waves. J. Fluid Mech. 92, 691–715 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  2. Babaoglu, C.: Long-wave short-wave resonance case for a generalized Davey–Stewartson system. Chaos Solitons Fractals 38, 48–54 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  3. Davey, A., Stewartson, K.: On three-dimensional packets of surface waves. Proc. R. Soc. Lond. A Math. Phys. Sci. 338, 101–110 (1974)

    MathSciNet  MATH  Google Scholar 

  4. Djordjevic, V.D., Redekopp, L.G.: On two-dimensional packets of capillary-gravity waves. J. Fluid Mech. 79, 703–714 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  5. Song, L.M., Yang, Z.J., Pang, Z.G., Li, X.L., Zhang, S.M.: Interaction theory of mirror-symmetry soliton pairs in nonlocal nonlinear Schrodinger equation. Appl. Math. Lett. 90, 42–48 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  6. Song, L.M., Yang, Z.J., Li, X.L., Zhang, S.M.: Controllable Gaussian-shaped soliton clusters in strongly nonlocal media. Opt. Express 26, 19182–19198 (2018)

    Article  Google Scholar 

  7. Song, L.M., Yang, Z.J., Zhang, S.M., Li, X.L.: Spiraling anomalous vortex beam arrays in strongly nonlocal nonlinear media. Phys. Rev. A 99, 063817 (2019)

    Article  Google Scholar 

  8. Hasimoto, H., Ono, H.: Nonlinear modulation of gravity waves. J. Phys. Soc. Jpn. 33, 805–811 (1972)

    Article  Google Scholar 

  9. Chan, H.N., Ding, E., Kedziora, D.J., Grimshaw, R., Chow, K.W.: Rogue waves for a long wave-short wave resonance model with multiple short waves. Nonlinear Dyn. 85, 1–15 (2016)

    Article  MathSciNet  Google Scholar 

  10. Zhai, Y., Geng, X., Xue, B.: Riemann theta function solutions to the coupled long wave-short wave resonance equations. Anal. Math. Phys. 56, 1–26 (2020)

    MathSciNet  MATH  Google Scholar 

  11. Benney, D.J.: A general theory for interactions between short and long waves. Stud. Appl. Math. 56, 81–94 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  12. Wright, O.C., III.: On a homoclinic manifold of a coupled long-wave-short-wave system. Commun. Nonlinear Sci. Numer. Simul. 15, 2066–2072 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  13. Wang, C., Dai, Z.: Various breathers and rogue waves for the coupled long-wave-short-wave system. Adv. Differ. Equ. 2014, 1–10 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  14. Chen, W., Chen, H., Dai, Z.: Rational homoclinic solution and rogue wave solution for the coupled long-wave-short-wave system. Pramana 86, 713–717 (2016)

    Article  Google Scholar 

  15. Wang, X.M., Zhang, L.L., Hu, X.X.: Various types of vector solitons for the coupled nonlinear Schrödinger equations in the asymmetric fiber couplers. Optik 219, 164989 (2020)

    Article  Google Scholar 

  16. Wang, X.M., Zhang, L.L.: The nonautonomous N-soliton solutions for coupled nonlinear Schrödinger equation with arbitrary time-dependent potential. Nonlinear Dyn. 88, 2291–2302 (2017)

    Article  Google Scholar 

  17. Zhang, F.: Intelligent task allocation method based on improved QPSO in multi-agent system. J. Ambient Intell. Humumaz. Comput. 11, 655–662 (2020)

    Article  Google Scholar 

  18. Fu, Y., Kumar, J., Ganthia, B.P., Neware, R.: Nonlinear dynamic measurement method of software reliability based on data mining. Int. J. Syst. Assur. Eng. Manag. (2021). https://doi.org/10.1007/s13198-021-01389-0

  19. Pei, S., Ye, L., Zhou, W.: Application of convolutional neural network under nonlinear excitation function in the construction of employee incentive and constraint mode. Int. J. Syst. Assur. Eng. Manag. (2021). https://doi.org/10.1007/s13198-021-01511-2

  20. Chen, J., Bian, L., Kumar, A., Neware, R.: A research based on application of dimension reduction technology in data visualization using machine learning. Int. J. Syst. Assur. Eng. Manag. (2021). https://doi.org/10.1007/s13198-021-01401-7

  21. Fan, M., Su, D., Bhatt, M.W., Mangal, A.: Study on non-linear planning model of green building energy consumption under multi-objective optimization. Int. J. Syst. Assur. Eng. Manag. (2021). https://doi.org/10.1007/s13198-021-01459-3

  22. Sam, I.S., Devaraj, P., Bhuvaneswaran, R.S.: An efficient quasigroup based image encryption using modified nonlinear chaotic maps. Sens. Imaging 15, 1–21 (2014)

    Article  Google Scholar 

  23. Guo, R., Hao, H.Q.: Breathers and multi-soliton solutions for the higher-order generalized nonlinear Schrödinger equation. Commun. Nonlinear Sci. Numer. Simul. 18, 2426–2435 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  24. Hao, H.Q., Zhang, J.W.: Integrability aspects and soliton solutions for the inhomogeneous reduced Maxwell-Bloch system in nonlinear optics with symbolic computation. Commun. Nonlinear Sci. Numer. Simul. 22, 1350–1359 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  25. Radgolchin, M., Tahani, M.: Nonlinear vibration analysis of beam microgyroscopes using nonlocal strain gradient theory. Sens. Imaging 22, 1–25 (2021)

    Article  Google Scholar 

  26. Rigatos, G., Siano, P., Zervos, N.: An approach to fault diagnosis of nonlinear systems using neural networks with invariance to Fourier transform. J. Ambient Intell. Humaniz. Comput. 4, 621–639 (2013)

    Article  Google Scholar 

  27. Zhu, Q., Lin, F., Li, H., Hao, R.: Human-autonomous devices for weak signal detection method based on multimedia chaos theory. J. Ambient Intell. Humaniz. Comput. (2020). https://doi.org/10.1007/s12652-020-02270-x

  28. Ambikapathy, B., Krishnamurthy, K.: Analysis of electromyograms recorded using invasive and noninvasive electrodes: a study based on entropy and Lyapunov exponents estimated using artificial neural networks. J. Ambinet Intell. Humaniz. Comput. 1–9 (2018)

  29. Azizi, S., Javaheri, H., Ghanati, P.: On the nonlinear dynamics of a tunable shock micro-switch. Sens. Imaging 17, 1–11 (2016)

    Article  Google Scholar 

  30. Mollabashi, H.E., Mazinan, A.H.: On stability analysis of a class of nonlinear systems with a focus on composite nonlinear feedback approach. Sens. Imaging 19, 1–12 (2018)

    Article  Google Scholar 

  31. Tajiri, M., Takeuchi, K., Arai, T.: Asynchronous development of the Benjamin–Feir unstable mode: solution of the Davey–Stewartson equation. Phys. Rev. E 64, 056622 (2001)

    Article  Google Scholar 

  32. Tajiri, M., Arai, T.: Quasi-line soliton interactions of the Davey–Stewartson I equation: on the existence of long-range interaction between two quasi-line solitons through a periodic soliton. J. Phys. A Math. Theor. 44, 235204 (2011)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

We express our sincere thanks to each member of our discussion group for their suggestions. This work has been supported by the National Natural Science Foundation of China under Grant No. 11905155 and the Shanxi Province Science Foundation for Youths, China, under Grant Nos. 201801D221023 and 201801D121016.

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Authors and Affiliations

  1. School of Mathematics, Taiyuan University of Technology, Taiyuan, 030024, China

    Kuai Bi, Hui-Qin Hao, Jian-Wen Zhang & Rui Guo

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  1. Kuai Bi
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  2. Hui-Qin Hao
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  3. Jian-Wen Zhang
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  4. Rui Guo
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Correspondence to Hui-Qin Hao.

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Bi, K., Hao, HQ., Zhang, JW. et al. Soliton, breather-like and dark-soliton-breather-like solutions for the coupled long-wave–short-wave system. Nonlinear Dyn 108, 543–554 (2022). https://doi.org/10.1007/s11071-022-07209-9

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