Modulation Instability, N-Solitons, Resonant Multi-Wave Structures and Other Diverse Interaction Phenomena to the (2+1)-Dimensional Kadomtsev-Petviashvili-BenjaminBona-Mahony Equation

• Muhammad Naveed Rafiq ^[1] ; Haibo Chen ^[1]
  1. [1] Central South University

     Central South University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 1, 2025
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • Nonlinear science is a key area of scientific research dedicated to studying the fundamental properties and common features of nonlinear phenomena. This study specifically investigates the (2+1)-dimensional Kadomtsev-Petviashvili-BenjaminBona-Mahony (KP-BBM) equation in nonlinear dispersive systems. By employing the Hirota bilinear method along with the linear superposition principle to the bilinear form of this equation, various new wave structures are effectively derived, such as N-solitons, resonance-type solitons, hybrid interaction solutions, and resonant multiwave solutions. To ensure the physical compatibility of the results, we generated 3D and density plots using appropriate parametric values, which will provide effective insights into the obtained wave solutions. Moreover, we provide a modulation instability analysis of the KP-BBM equation with its stability region. The novelty of this work lies in the fact that the results discussed are new and have not been previously explored for the given equation. Additionally, the methods applied are efficient and reliable for constructing new soliton wave solutions in nonlinear physical phenomena.

    We predict that the findings of this study will have significant applications in optical fibers, plasma physics, engineering and fluid dynamics.

• Referencias bibliográficas
  • 1. Kumar, S., Mann, N.: A variety of newly formed soliton solutions and patterns of dynamic waveforms for the generalized complex coupled...
  • 2. Shen, Y., Tian, B., Cheng, C.D., Zhou, T.Y.: Pfaffian solutions and nonlinear waves of a (3+ 1)- dimensional generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt...
  • 3. Khater, M.M.: Analyzing the physical behavior of optical fiber pulses using solitary wave solutions of the perturbed Chen-Lee-Liu equation....
  • 4. Yusuf, A., Sulaiman, T.A., Abdeljabbar, A., Alquran, M.: Breather waves, analytical solutions and conservation laws using Lie-Bäcklund...
  • 5. Khater, M.M.: Exploring the rich solution landscape of the generalized Kawahara equation: insights from analytical techniques. The European...
  • 6. Alhami, R., Alquran, M.: Extracted different types of optical lumps and breathers to the new generalized stochastic potential-KdV equation...
  • 7. Shen, Y., Tian, B., Zhou, T.Y.: Studies on an extended (3+1)-dimensional variable-coefficient shallow water wave equation: Bilinear...
  • 8. Khater, M.M.: Wave propagation analysis in the modified nonlinear time fractional harry dym equation: Insights from khater II method and...
  • 9. Khater, M.M.: Computational method for obtaining solitary wave solutions of the (2+ 1)-dimensional AKNS equation and their physical...
  • 10. Kumar, S., Kukkar, A.: Dynamics of several optical soliton solutions of a (3+ 1)-dimensional nonlinear Schrödinger equation with parabolic...
  • 11. Lin, Y., Khater, M.M.: Plenty of accurate, explicit solitary unidirectional wave solutions of the nonlinear Gilson-Pickering model. International...
  • 12. Gu, C.: editor. Soliton theory and its applications. Springer Science & Business Media; (2013)
  • 13. Fordy, A.P.: editor. Soliton theory: a survey of results. Manchester University Press; (1990)
  • 14. Raza, N., Javid, A.: Dynamics of optical solitons with Radhakrishnan-Kundu-Lakshmanan model via two reliable integration schemes. Optik....
  • 15. Mann, N., Kumar, S., Ma, W.X.: Dynamics of analytical solutions and Soliton-like profiles for the nonlinear complex-coupled Higgs field...
  • 16. Khater, M.M., Alfalqi, S.H.: Solitary wave solutions for the (1+ 1)-dimensional nonlinear KakutaniMatsuuchi model of internal gravity...
  • 17. Khater, M.M.: Dynamic insights into nonlinear evolution: Analytical exploration of a modified widthBurgers equation. Chaos, Solitons &...
  • 18. Heimburg, T., Jackson, A.D.: On soliton propagation in biomembranes and nerves. Proceedings of the National Academy of Sciences. 102(28),...
  • 19. Nakazawa, M., Kubota, H., Suzuki, K., Yamada, E., Sahara, A.: Recent progress in soliton transmission technology. Chaos: An Interdisciplinary...
  • 20. Shen, Y., Tian, B., Cheng, C.D., Zhou, T.Y.: N-soliton, Mth-order breather, H th-order lump, and hybrid solutions of an extended (3+...
  • 21. Kumar, S., Mohan, B.: A study of multi-soliton solutions, breather, lumps, and their interactions for kadomtsev-petviashvili equation...
  • 22. Raza, N., Jhangeer, A., Rahman, R.U., Butt, A.R., Chu, Y.M.: Sensitive visualization of the fractional Wazwaz-Benjamin-Bona-Mahony equation...
  • 23. Novikov, S., Manakov, S.V., Pitaevskii, L.P., Zakharov, V.E.: Theory of solitons: the inverse scattering method. Springer Science &...
  • 24. Alquran, M., Alhami, R.: Analysis of lumps, single-stripe, breather-wave, and two-wave solutions to the generalized perturbed-KdV equation...
  • 25. Shen, Y., Tian, B., Cheng, C.D., Zhou, T.Y.: Interactions of certain localized waves for an extended (3+ 1)-dimensional Kadomtsev-Petviashvili...
  • 26. Yan, X.W., Chen, Y.: Rogue wave patterns of the Fokas-Lenells equation. Europhysics Letters. 144(6), 62001 (2024)
  • 27. Kumar, S., Mohan, B.: A generalized nonlinear fifth-order KdV-type equation with multiple soliton solutions: Painlevé analysis and Hirota...
  • 28. Rafiq, M.H., Jhangeer, A., Raza, N.: The analysis of solitonic, supernonlinear, periodic, quasiperiodic, bifurcation and chaotic patterns...
  • 29. Rafiq, M.H., Jannat, N., Rafiq, M.N.: Sensitivity analysis and analytical study of the three-component coupled NLS-type equations in fiber...
  • 30. Rafiq, M.N., Chen, H., Rafiq, M.H.: Stability analysis and multi-wave structures of the ill-posed Boussinesq equation arising in nonlinear...
  • 31. Gai, L., Ma, W.X., Li, M.: Lump-type solutions, rogue wave type solutions and periodic lump-stripe interaction phenomena to a (3+...
  • 32. Yusuf, A., Sulaiman, T.A., Abdeljabbar, A., Alquran, M.: Breather waves, analytical solutions and conservation laws using Lie-Bäcklund...
  • 33. Seadawy, A.R., Rizvi, S.T., Ahmed, S., Bashir, A.: Lump solutions, Kuznetsov-Ma breathers, rogue waves and interaction solutions for magneto...
  • 34. Rafiq, M.N., Chen, H.: Multiple interaction solutions, parameter analysis, chaotic phenomena and modulation instability for a (3+...
  • 35. Wadati, M.: Introduction to solitons. Pramana. 57, 841–7 (2001)
  • 36. Kadomtsev, B.B., Petviashvili, V.I.: On the stability of the KP equation and application to shallow water waves. Soviet Physics, JETP....
  • 37. Mia, R., Miah, M.M., Osman, M.S.: A new implementation of a novel analytical method for finding the analytical solutions of the (2+...
  • 38. Wazwaz, A.M.: The extended tanh method for new compact and noncompact solutions for the KP-BBM and the ZK-BBM equations. Chaos, Solitons,...
  • 39. Yu, Y., Ma, H.C.: Explicit solutions of (2+ 1)-dimensional nonlinear KP-BBM equation by using Exp-function method. Applied Mathematics...
  • 40. Song, M., Liu, Z., Biswas, A.: Soliton solution and bifurcation analysis of the KP-Benjamin-BonaMahoney equation with power law nonlinearity....
  • 41. Manafian, J., Murad, M.A., Alizadeh, A.A., Jafarmadar, S.: M-lump, interaction between lumps and stripe solitons solutions to the (2+...
  • 42. Wazwaz, A.M.: Exact solutions of compact and noncompact structures for the KP-BBM equation. Applied Mathematics & Computation. 169(1),...
  • 43. Ma, W.X.: Bilinear equations, Bell polynomials and linear superposition principle. Journal of Physics: Conference Series. 411(1), 012021...
  • 44. Ma, W.X., Zhou, Y.: Lump solutions to nonlinear partial differential equations via Hirota bilinear forms. Journal of Differential Equations....
  • 45. Ma, W.X.: Generalized bilinear differential equations. Studies in Nonlinear Sciences. 2(4), 140–4 (2011)
  • 46. Hirota, R., Ito, M.: Resonance of solitons in one dimension. Journal of the Physical Society of Japan. 52(3), 744–8 (1983)
  • 47. He, L., Zhang, J., Zhao, Z.: Resonance Y-type soliton, hybrid and quasi-periodic wave solutions of a generalized (2+ 1)-dimensional...
  • 48. Rafiq, M.H., Raza, N., Jhangeer, A.: Dynamic study of bifurcation, chaotic behavior and multi-soliton profiles for the system of shallow...
  • 49. Rafiq, M.N., Chen, H.: Dynamics of three-wave solitons and other localized wave solutions to a new generalized (3+ 1)-dimensional...
  • 50. Rafiq, M.H., Riaz, M.B., Basendwah, G.A., Raza, N., Rafiq, M.N.: Dynamics of quasi-periodic, bifurcation, sensitivity and three-wave solutions...
  • 51. Mann, N., Rani, S., Kumar, S., Kumar, R.: Novel closed-form analytical solutions and modulation instability spectrum induced by the Salerno...