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Space-curved resonant solitons and inelastic interaction solutions of a (2+1)-dimensional generalized KdV equation

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Abstract

The nonlinear phenomenon of space-curved resonant solitons is mainly focused on. An integrable (2+1)-dimensional generalized KdV equation in the sense of the Hirota’s bilinear method is considered to construct the interaction solutions consisting of multiple-space-curved resonant solitons. The characteristics including curvature, width and interaction dynamics of this kind of resonant soliton are studied systematically. The inelastic interaction solutions consisting of the space-curved resonant solitons and lump waves are obtained in virtue of the new constraints of parameters and the method of long wave limit. The amplitude of the lump wave significantly increases after collision with multiple-space-curved resonant solitons, which indicates a new mechanism for generating rogue waves. The results expand our understanding of the resonance of solitons and interaction dynamics of the nonlinear waves.

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References

  1. Zhao, L.C., Liu, C., Yang, Z.Y.: The rogue waves with quintic nonlinearity and nonlinear dispersion effects in nonlinear optical fibers. Commun. Nonlinear Sci. Numer. Simul. 20, 9–13 (2015)

    Article  ADS  Google Scholar 

  2. Baronio, F., Wabnitz, S., Kodama, Y.: Optical Kerr spatiotemporal dark-lump dynamics of hydrodynamic origin. Phys. Rev. Lett. 116, 173901 (2016)

    Article  ADS  PubMed  Google Scholar 

  3. Rulands, S., Klünder, B., Frey, E.: Stability of localized wave fronts in bistable systems. Phys. Rev. Lett. 110, 038102 (2013)

    Article  ADS  PubMed  Google Scholar 

  4. Yang, D.Y., Tian, B., Qu, Q.X., Zhang, C.R., Chen, S.S., Wei, C.C.: Lax pair, conservation laws, Darboux transformation and localized waves of a variable-coefficient coupled Hirota system in an inhomogeneous optical fiber. Chaos, Solitons Fractals 150, 110487 (2021)

    Article  MathSciNet  Google Scholar 

  5. Shukla, P.K.: Nonlinear waves and structures in dusty plasmas. Phys. Plasmas 10, 1619–1627 (2003)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  6. Ahmad, S., Mahmoud, E.E., Saifullah, S., Ullah, A., Ahmad, S., Akgül, A., El Din, S.M.: New waves solutions of a nonlinear Landau-Ginzburg-Higgs equation: the Sardar-subequation and energy balance approaches. Results Phys. 51, 106736 (2023)

    Article  Google Scholar 

  7. Ahmad, S., Saifullah, S., Khan, A.: Inc, M: new local and nonlocal soliton solutions of a nonlocal reverse space-time mKdV equation using improved Hirota bilinear method. Phys. Lett. A 450, 128393 (2022)

    Article  CAS  Google Scholar 

  8. Yan, Z.Y., Konotop, V.V., Akhmediev, N.: Three-dimensional rogue waves in nonstationary parabolic potentials. Phys. Rev. E 82, 036610 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  9. Zhou, Q., Triki, H., Xu, J.K., Zeng, Z.L., Liu, W.J., Biswas, A.: Perturbation of chirped localized waves in a dual-power law nonlinear medium. Chaos, Solitons Fractals 160, 112198 (2022)

    Article  MathSciNet  Google Scholar 

  10. Chen, J.B., Pelinovsky, D.E.: Periodic waves in the discrete mKdV equation: modulational instability and rogue waves. Phys. D 445, 133652 (2023)

    Article  MathSciNet  Google Scholar 

  11. Yue, Y.F., Huang, L.L., Chen, Y.: Localized waves and interaction solutions to an extended (3+1)-dimensional Jimbo-Miwa equation. Appl. Math. Lett. 89, 70–77 (2019)

    Article  MathSciNet  Google Scholar 

  12. Xu, Y.S., Mihalache, D., He, J.S.: Resonant collisions among two-dimensional localized waves in the Mel’nikov equation. Nonlinear Dyn. 106, 2431–2448 (2021)

    Article  Google Scholar 

  13. 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 

  14. Xu, G.Q., Wazwaz, A.M.: Integrability aspects and localized wave solutions for a new (4+1)-dimensional Boiti-Leon-Manna-Pempinelli equation. Nonlinear Dyn. 98, 1379–1390 (2019)

    Article  Google Scholar 

  15. Feng, B.F., Shi, C.Y., Zhang, G.X., Wu, C.F.: Higher-order rogue wave solutions of the Sasa-Satsuma equation. J. Phys. A Math. Theor. 55, 235701 (2022)

    Article  ADS  MathSciNet  Google Scholar 

  16. Saifullah, S., Ahmad, S., Alyami, M.A., Inc, M.: Multiple bifurcation solitons, lumps and rogue waves solutions of a generalized perturbed KdV equation. Phys. Lett. A 454, 128503 (2022)

    Article  CAS  Google Scholar 

  17. Khan, A., Saifullah, S., Ahmad, S., Khan, J., Baleanu, D.: Multiple bifurcation solitons, lumps and rogue waves solutions of a generalized perturbed KdV equation. Nonlinear Dyn. 111, 5743–5756 (2023)

    Article  Google Scholar 

  18. Kee, C.S., Li, S.Z., Kim, K., Lim, H.: Tunable resonant transmission of electromagnetic waves through a magnetized plasma. Phys. Rev. E 67, 036612 (2003)

    Article  ADS  Google Scholar 

  19. Yin, Z.Q., Li, F.L.: Multiatom and resonant interaction scheme for quantum state transfer and logical gates between two remote cavities via an optical fiber. Phys. Rev. A 75, 012324 (2007)

    Article  ADS  Google Scholar 

  20. Ngo, Q.M., Hoang, T.T., Nguyen, D.L., Vu, D.L., Pham, V.H.: Metallic assisted guided-mode resonances in slab waveguide gratings for reduced optical switching intensity in bistable devices. J. Opt. 15, 055503 (2013)

    Article  ADS  CAS  Google Scholar 

  21. Ahmad, S., Saifullah, S., Khan, A., Wazwaz, A.M.: Resonance, fusion and fission dynamics of bifurcation solitons and hybrid rogue wave structures of Sawada-Kotera equation. Commun. Nonlinear Sci. Numer. Simul. 119, 107117 (2023)

    Article  MathSciNet  Google Scholar 

  22. Ablowitz, M.J., Baldwin, D.E.: Nonlinear shallow ocean-wave soliton interactions on flat beaches. Phys. Rev. E 86, 036305 (2012)

    Article  ADS  Google Scholar 

  23. Kodama, Y.: KP Solitons and the Grassmannians: Combinatorics and Geometry of Two-Dimensional Wave Patterns. Springer, Berlin (2017)

    Book  Google Scholar 

  24. Lester, C., Gelash, A., Zakharov, D., Zakharov, V.: Lump chains in the KP-I equation. Stud. Appl. Math. 147, 1425–1442 (2021)

    Article  MathSciNet  Google Scholar 

  25. Zhao, Z.L., He, L.C., Wazwaz, A.M.: Dynamics of lump chains for the BKP equation describing propagation of nonlinear waves. Chin. Phys. B 32, 040501 (2023)

    Article  ADS  Google Scholar 

  26. Qi, Z.Q., Zhang, Z., Li, B.: Space-curved resonant line solitons in a generalized (2+1)-dimensional fifth-order KdV system. Chin. Phys. Lett. 38, 060501 (2021)

    Article  ADS  Google Scholar 

  27. Zhao, Z.L., Zhang, C.F., Feng, Y.X., Yue, J.: Space-curved resonant solitons and interaction solutions of the (2+1)-dimensional Ito equation. Appl. Math. Lett. 146, 108799 (2023)

    Article  MathSciNet  Google Scholar 

  28. Lü, X., Chen, S.J.: Interaction solutions to nonlinear partial differential equations via Hirota bilinear forms: one-lump-multi-stripe and one-lump-multi-soliton types. Nonlinear Dyn. 103, 947–977 (2021)

    Article  Google Scholar 

  29. Lü, X., Chen, S.J.: N-soliton solutions and associated integrability for a novel (2+1)-dimensional generalized KdV equation. Chaos, Solitons Fractals 169, 113291 (2023)

  30. Ablowitz, M.J., Satsuma, J.: Solitons and rational solutions of nonlinear evolution equations. J. Math. Phys. 19, 2180–2186 (1978)

    Article  ADS  MathSciNet  Google Scholar 

  31. Zhao, Z.L., He, L.C.: Nonlinear superposition between lump waves and other waves of the (2+1)-dimensional asymmetrical Nizhnik-Novikov-Veselov equation. Nonlinear Dyn. 108, 555–568 (2022)

    Article  Google Scholar 

  32. Zhao, Z.L., He, L.C.: M-lump and hybrid solutions of a generalized (2+1)-dimensional Hirota-Satsuma-Ito equation. Appl. Math. Lett. 111, 106612 (2021)

    Article  MathSciNet  Google Scholar 

  33. Zhang, Z., Yang, X.Y., Li, B., Guo, Q., Stepanyants, Y.: Multi-lump formations from lump chains and plane solitons in the KP1 equation. Nonlinear Dyn. 111, 1625–1642 (2023)

    Article  Google Scholar 

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Nos. 12101572 and 12371256) and Research Project Supported by Shanxi Scholarship Council of China (No. 2020-105).

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Authors and Affiliations

  1. School of Mathematics, North University of China, Taiyuan, 030051, Shanxi, People’s Republic of China

    Zhonglong Zhao

  2. College of Mathematics, Taiyuan University of Technology, Taiyuan, 030024, Shanxi, People’s Republic of China

    Lingchao He

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Zhao, Z., He, L. Space-curved resonant solitons and inelastic interaction solutions of a (2+1)-dimensional generalized KdV equation. Nonlinear Dyn 112, 3823–3833 (2024). https://doi.org/10.1007/s11071-023-09223-x

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  • DOI: https://doi.org/10.1007/s11071-023-09223-x

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