Skip to main content
SpringerLink
Log in

Periodic bright–dark soliton, breather-like wave and rogue wave solutions to a \({\bar{p}}\)-GBS equation in (3+1)-dimensions

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

This paper aims to present a trilinear neural network method on the basis of the trilinear form of a (3+1)-dimensional \({\bar{p}}\)-GBS equation. This method can be used to construct new exact traveling wave solutions. We set the hidden neurons in three types of tensor functions to some specific functions, and reach a class of periodic bright–dark soliton solutions, two types of breather-like wave solutions and three types of rogue wave solutions for \({\bar{p}}\)-GBS equation successfully. The 3-D and density graphs of those solutions obtained are given to interpret the dynamic characteristics.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

Data availability

Data sharing is not applicable to this article as no datasets were generated or analyzed during the current study.

References

  1. Zhou, Y., Zhang, X.J., Zhang, C., Jia, J.J., Ma, W.X.: New lump solutions to a (3+1)-dimensional generalized Calogero–Bogoyavlenskii–Schiff equation. Appl. Math. Lett. 141, 108598 (2023)

    Article  MathSciNet  MATH  Google Scholar 

  2. Gai, L.T., Ma, W.X., Li, M.C.: Lump-type solutions, rogue wave type solutions and periodic lump-stripe interaction phenomena to a (3+1)-dimensional generalized breaking soliton equation. Phys. Lett. A 384, 126178 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  3. Zhao, Z.L., He, L.C.: Multiple lump solutions of the (3+1)-dimensional potential Yu–Toda–Sasa–Fukuyama equation. Appl. Math. Lett. 95, 114–121 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  4. Musammil, N.M., Subha, P.A., Nithyanandan, K.: Phase dynamics of inhomogeneous Manakov vector solitons. Phys. Rev. E 100, 012213 (2019)

    Article  Google Scholar 

  5. Cheng, L., Zhang, Y., Ma, W.X.: Wronskian \(N\)-soliton solutions to a generalized KdV equation in (2+1)-dimensions. Nonlinear Dyn. 111, 1701–1714 (2023)

    Article  Google Scholar 

  6. Wazwaz, A.-M.: New (3+1)-dimensional Painlevé integrable fifth-order equation with third-order temporal dispersion. Nonlinear Dyn. 106, 891–897 (2021)

    Article  Google Scholar 

  7. Wazwaz, A.-M.: Painlevé integrability and lump solutions for two extended (3+1)- and (2+1)-dimensional Kadomtsev–Petviashvili equations. Nonlinear Dyn. 111, 3623–3632 (2023)

    Article  Google Scholar 

  8. Wang, T.G., Qin, Z.Y., Mu, G., Zheng, F.Z.: General high-order rogue waves in the Hirota equation. Appl. Math. Lett. 140, 108571 (2023)

    Article  MathSciNet  MATH  Google Scholar 

  9. Su, J.J., Gao, Y.T., Deng, G.F., Jia, T.T.: Solitary waves, breathers, and rogue waves modulated by long waves for a model of a baroclinic shear flow. Phys. Rev. E 100, 042210 (2019)

    Article  MathSciNet  Google Scholar 

  10. Qin, Y.X., Liu, Y.P.: Multiwave interaction solutions for a (3+1)-dimensional generalized Kadomtsev–Petviashvili equation. Chin. J. Phys. 71, 561–573 (2021)

    Article  MathSciNet  Google Scholar 

  11. Ma, W.X.: Trilinear equations, Bell polynomials, and resonant solutions. Front. Math. Chin. 8, 1139–1156 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  12. Gai, L.T., Ma, W.X., Li, M.C.: Lump-type solution and breather lump-kink interaction phenomena to a (3+1)-dimensional GBK equation based on trilinear form. Nonlinear Dyn. 100, 2715–2727 (2020)

    Article  Google Scholar 

  13. Gai, L.T., Li, M.C.: A trilinear analysis for lump-type wave, breather wave and BK-type wave solutions of a (3+1)-dimensional p-gKP equation. Chin. J. Phys. 72, 38–49 (2021)

    Article  MathSciNet  Google Scholar 

  14. Zhang, R.F., Li, M.C., Albishari, M., Zheng, F.C., Lan, Z.Z.: Generalized lump solutions, classical lump solutions and rogue waves of the (2+1)-dimensional Caudrey–Dodd–Gibbon–Kotera–Sawada-like equation. Appl. Math. Comput. 403, 126201 (2021)

    MathSciNet  MATH  Google Scholar 

  15. Zhang, R.F., Li, M.C., Yin, H.M.: Rogue wave solutions and the bright and dark solitons of the (3+1)-dimensional Jimbo–Miwa equation. Nonlinear Dyn. 103, 1071–1079 (2021)

    Article  Google Scholar 

  16. Zhang, R.F., Sudao, B.: Bilinear neural network method to obtain the exact analytical solutions of nonlinear partial differential equations and its application to p-gBKP equation. Nonlinear Dyn. 95, 3041–3048 (2019)

    Article  MATH  Google Scholar 

  17. Zhang, R.F., Li, M.C.: Bilinear residual network method for solving the exactly explicit solutions of nonlinear evolution equations. Nonlinear Dyn. 108, 521–531 (2022)

    Article  Google Scholar 

  18. Zhang, R.F., Li, M.C., Cherraf, A., Vadyala, S.R.: The interference wave and the bright and dark soliton for two integro-differential equation by using BNNM. Nonlinear Dyn. 111, 8637–8646 (2023)

    Article  Google Scholar 

  19. Gai, L.T., Ma, W.X., Sudao, B.: Abundant multilayer network model solutions and bright–dark solitons for a (3+1)-dimensional \(p\)-gBLMP equation. Nonlinear Dyn. 106, 867–877 (2021)

    Article  Google Scholar 

  20. Ma, Y.L., Li, B.Q.: Interactions between soliton and rogue wave for a (2+1)-dimensional generalized breaking soliton system: hidden rogue wave and hidden soliton. Comput. Math. Appl. 78, 827–839 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  21. Chen, R.D., Gao, Y.T., Yu, X., Jia, T.T., Deng, G.F., Liu, F.Y.: Periodic-wave solutions and asymptotic properties for a (3+1)-dimensional generalized breaking soliton equation in fluids and plasmas. Mod. Phys. Lett. B 35, 2150344 (2021)

    Article  MathSciNet  Google Scholar 

  22. Ma, W.X.: Bilinear equations, Bell polynomials and linear superposition principle. J. Phys.: Conf. Ser 411, 012021 (2013)

    Google Scholar 

  23. Peng, W.Q., Chen, Y.: \(N\)-double poles solutions for nonlocal Hirota equation with nonzero boundary conditions using Riemann–Hilbert method and PINN algorithm. Phys. D 435, 133274 (2022)

    Article  MathSciNet  MATH  Google Scholar 

  24. Pu, J.C., Chen, Y.: Data-driven forward-inverse problems for Yajima–Oikawa system using deep learning with parameter regularization. Commun. Nonlinear Sci. Numer. Simul. 118, 107051 (2023)

  25. Wazwaz, A.-M., Albalawi, W., El-Tantawy, S.A.: Optical envelope soliton solutions for coupled nonlinear Schrödinger equations applicable to high birefringence fibers. Optik 255, 168673 (2022)

    Article  Google Scholar 

  26. Wazwaz, A.-M., Hammad, M.A., El-Tantawy, S.A.: Bright and dark optical solitons for (3+1)-dimensional hyperbolic nonlinear Schrödinger equation using a variety of distinct schemes. Optik 270, 170043 (2022)

    Article  Google Scholar 

  27. Kaur, L., Wazwaz, A.-M.: Optical soliton solutions of variable coefficient Biswas–Milovic (BM) model comprising Kerr law and damping effect. Optik 266, 169617 (2022)

    Article  Google Scholar 

  28. Kumar, S., Dhiman, S.K., Baleanu, D., Osman, S.M., Wazwaz, A.-M.: Lie symmetries, closed-form solutions, and various dynamical profiles of solitons for the variable coefficient (2+1)-dimensional KP equations. Symmetry 14, 597 (2022)

    Article  Google Scholar 

  29. Salah, M., Ragb, O., Wazwaz, A.-M.: Efficient discrete singular convolution differential quadrature algorithm for solitary wave solutions for higher dimensions in shallow water waves, Wave Ran. Comp., 1-18 (2022)

Download references

Acknowledgements

The work was supported in part by the National Natural Science Foundation of China through grant No. 12172333, the Natural Science Foundation of Zhejiang through grant No. LY20A020003, the Key Scientific and Technological Project of Henan Province (Grant Nos. 212102210324 and 212102210432), and the Postdoctoral Research Foundation of China through grant No. ZC304122901.

Author information

Authors and Affiliations

  1. School of Mathematical Sciences, Zhejiang Normal University, Jinhua, 321004, Zhejiang, China

    Litao Gai & Youhua Qian

  2. School of Science, Henan Institute of Technology, Xinxiang, 453003, Henan, China

    Yupeng Qin

  3. School of Software Technology, Dalian University of Technology, Dalian, 116620, China

    Runfa Zhang

Authors
  1. Litao Gai
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Youhua Qian
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yupeng Qin
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Runfa Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Youhua Qian.

Ethics declarations

Competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gai, L., Qian, Y., Qin, Y. et al. Periodic bright–dark soliton, breather-like wave and rogue wave solutions to a \({\bar{p}}\)-GBS equation in (3+1)-dimensions. Nonlinear Dyn 111, 15335–15346 (2023). https://doi.org/10.1007/s11071-023-08628-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-023-08628-y

Keywords

Search

Navigation