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A Study of a (3+1)-Dimensional Hirota Bilinear Model with Variable Coefficients: Generalized Higher-Order Rogue Waves and Wronskian Solutions

  • Majid Madadi [2] ; Mustafa Inc [1]
    1. [1] Biruni University

      Biruni University

      Turquía

    2. [2] Institute for Advanced Studies in Basic Sciences (IASBS)
  • Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 3, 2025
  • Idioma: inglés
  • Enlaces
  • Resumen

    • The Hirota bilinear equation with variable coefficients (VCs) serves as a fundamental model for capturing nonlinear wave dynamics in fluids and oceans. Utilizing the Hirota bilinear framework alongside advanced symbolic computation techniques, higherorder rational solutions to this equation have been comprehensively investigated. These solutions unveil a wide range of waveforms, including multi-rogue waves (RWs) and multi-parallel solitons. To further expand the solution space, the rational solutions have been generalized by introducing two adjustable parameters, α and β, referred to as center control parameters. These parameters enable the generation of a versatile class of nonlinear, controllable RWs, enhancing the flexibility and applicability of the model. Soliton solutions have also been constructed using the Wronskian method, with their validity rigorously established through proofs grounded in Plücker relations.

      By employing various functional forms for the VCs, the dynamic properties of these solutions have been extensively analyzed and visualized through three-dimensional representations, showcasing their rich complexity and diverse behaviors.

  • Referencias bibliográficas
    • 1. Hayer, S., Andersen, O.J.: Freak waves: rare realizations of a typical population or typical realizations of a rare population. ISOPE Conf....
    • 2. Dysthe, K., Krogstad, H.E., Müller, P.: Oceanic rogue waves. Annu. Rev. Fluid Mech. 40, 287–310 (2008)
    • 3. Ankiewicz, A., Devine, N.: Akhmediev,: Are rogue waves robust against perturbations. Phys. Lett. A. 43, 3997–4000 (2009)
    • 4. Janssen, P.A.E.M.: Nonlinear four-wave interactions and freak waves. J. Phys. Oceanogr. 33, 863–884 (2003)
    • 5. Ohta, Y., Yang, J.: General high-order rogue waves and their dynamics in the nonlinear Schrödinger equation. Proc. R. Soc. A. 468, 1716–1740...
    • 6. Chu, J., Liu, Y., Zhuang, J.: Painlevé analysis, Gram determinant solution and the dynamic behavior of the (2+ 1)-dimensional variable-coefficient...
    • 7. Yan, X.W., Tian, S.F., Dong, M.J., Zou, L.: Bäcklund transformation, rogue wave solutions and interaction phenomena for a (3+ 1)(3+...
    • 8. Cheng, C.D., Tian, B., Hu, C.C., Shen, Y.: Line-rogue waves, transformed nonlinear waves and their interactions for a (3+ 1)-dimensional...
    • 9. Yang, B., Yang, J.: Rogue waves in the nonlocal PT-symmetric nonlinear Schrödinger equation. Lett. Math. Phys. 109, 945–973 (2019)
    • 10. Zhang, X., Wang, Y.F., Yang, S.X.: Breathers, rogue waves, and interaction solutions for the variable coefficient Kundu-nonlinear Schrödinger...
    • 11. Clarkson, P.A., Dowie, E.: Rational solutions of the Boussinesq equation and applications to rogue waves. Trans. Math. Appl. 1, 1–26 (2017)
    • 12. Peregrine, D.H.: Water waves, nonlinear Schrödinger equations and their solutions. ANZIAM J. 25, 16–43 (1983)
    • 13. Kedziora, D.J., Ankiewicz, A., Akhmediev, N.: Classifying the hierarchy of nonlinear-Schrödingerequation rogue-wave solutions. Phys. Rev....
    • 14. Ablowitz, M., Segur, H.: Solitons and the inverse scattering transform. SIAM (1981)
    • 15. Ablowitz, M.J., Kaup, D.J., Newell, A.C., Segur, H.: The inverse scattering transform-Fourier analysis for nonlinear problems. Stud. Appl....
    • 16. Yasmin, H., Alshehry, A.S., Ganie, A.H., Mahnashi, A.M., Shah, R.: Perturbed Gerdjikov-Ivanov equation: Soliton solutions via Backlund...
    • 17. Wang, M., Li, N.: Painlevé Analysis and Soliton Solutions for an Inhomogeneous Heisenberg Ferromagnetic System. J. Nonlinear Math. Phys....
    • 18. Shen, Y., Tian, B., Zhou, T.Y., Cheng, C.D.: Complex Kraenkel-Manna-Merle system in a ferrite: N-fold Darboux transformation, generalized...
    • 19. Shen, Y., Tian, B., Zhou, T.Y., Cheng, C.D.: Localized waves of the higher-order nonlinear SchrödingerMaxwell-Bloch system with the sextic...
    • 20. Shen, Y.: An extended (3+ 1)-dimensional Bogoyavlensky-Konopelchenko equation: Pfaffian solutions and nonlinear wave interactions....
    • 21. Hirota, R.: The direct method in soliton theory. Cambridge University Press (2004)
    • 22. Ma, W.X.: Wronskians, generalized Wronskians and solutions to the Korteweg-de Vries equation. Chaos Solitons Fractals. 19, 163–170 (2004)
    • 23. Zhang, D.J., Zhao, S.L., Sun, Y.Y., Zhou, J.: Solutions to the modified Korteweg-de Vries equation. Rev. Math. Phys. 26, 1430006 (2014)
    • 24. Xu, T., Tian, B.: An extension of the Wronskian technique for the multicomponent Wronskian solution to the vector nonlinear Schrödinger...
    • 25. Cheng, C.D., Tian, B., Zhou, T.Y., Shen, Y.: Wronskian solutions and Pfaffianization for a (3+ 1)- dimensional generalized variable-coefficient...
    • 26. Ma, W.X., Li, C.X., He, J.: A second Wronskian formulation of the Boussinesq equation. Nonlinear Anal. 70, 4245–4258 (2009)
    • 27. Liu, J.G., Zhu, W.H.: Multiple rogue wave, breather wave and interaction solutions of a generalized (3+ 1)-dimensional variable-coefficient...
    • 28. Kumar, S., Dhiman, S.K., Baleanu, D., Osman, M.S., Wazwaz, A.M.: Lie symmetries, closed-form solutions, and various dynamical profiles...
    • 29. YH W.: Nonautonomous lump solutions for a variable–coefficient Kadomtsev–Petviashvili equation. Appl. Math. Lett. 119 1-17 (2021)
    • 30. Chen, Y.Q., Tian, B., Shen, Y., Zhou, T.Y.: Painlevé integrable property, Bäcklund transformations, Lax pair, and soliton solutions of...
    • 31. Hua, Y.F., Guo, B.L., Ma, W.X., Lü, X.: Interaction behavior associated with a generalized (2+ 1)- dimensional Hirota bilinear equation...
    • 32. Mandal, U.K.,Malik, S., Kumar, S., Das, A.: A generalized (2+ 1)-dimensional Hirota bilinear equation: integrability, solitons and...
    • 33. Hosseini, K., Samavat, M., Mirzazadeh, M., Ma, W.X., Hammouch, Z.: A new-dimensional Hirota bilinear equation: its Bäcklund transformation...
    • 34. Asadi, E., Hosseini, K., Madadi, M.: Superposition of soliton, breather and lump waves in a nonpainlevé integrabale extension of the Boiti-Leon-Manna-Pempinelli...
    • 35. Fokas, A.S., Ablowitz, M.J.: Linearization of the Korteweg-de Vries and Painlevé II Equations. Phys. Rev. Lett. 47, 1096 (1981)
    • 36. Whitham, G.B.: Linear and nonlinear waves. John Wiley & Sons (2011)
    • 37. Quispel, G.R.W., Nijhoff, F.W., Capel, H.W.: Linearization of the Boussinesq equation and the modified Boussinesq equation. Phys. Lett....
    • 38. Yablonskii, A.L.: On rational solutions of the second Painlevé equation. Vestsi Akad. Nauk BSSR, Ser. Fiz.-Tekh. Nauk. 3 30-35 (1959)
    • 39. Clarkson, P.A., Mansfield, E.L.: The second Painlevé equation, its hierarchy and associated special polynomials. Nonlinearity 16, 324–331...
    • 40. Okamoto, K.: Studies on the Painlevé equations: III. Second and fourth Painlevé equations, P II and P IV. Math. Ann. 275 221-255 (1986)
    • 41. Noumi,M., Yamada, Y.: Symmetries in the fourth Painlevé equation and Okamoto polynomials. Nagoya Math. J. 153, 53–86 (1999)
    • 42. Palamara, V., Neal, B., Akinyemi, L., Erebholo, F., Bogale, M.: Shallow-water waves through two new generalized multi-dimensional variable...
    • 43. Madadi, M., Inc, M.: Dynamics of localized waves and interactions in a (2+ 1)-dimensional equation from combined bilinear forms of...
    • 44. Nimmo, J.J.C., Freeman, N.C.: A method of obtaining the N-soliton solution of the Boussinesq equation in terms of a Wronskian. Phys. Lett....
    • 45. Freeman, N.C., Nimmo, J.J.C.: oliton solutions of the Korteweg de Vries and the KadomtsevPetviashvili equations: the Wronskian technique....
    • 46. Wang, X., Wei, J.: Antidark solitons and soliton molecules in a (3+ 1)-dimensional nonlinear evolution equation. Nonlinear Dyn. 102,...
    • 47. Wang, X., He, J.: Darboux transformation and general soliton solutions for the reverse space-time nonlocal short pulse equation. Physica...
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