The Integrability and Several Localized Wave Solutions of a Generalized (2+1)-Dimensional Nonlinear Wave Equation

• Huilin Cui ^[1] ; Yexuan Feng ^[1] ; Zhonglong Zhao ^[1]
  1. [1] North University of China

     North University of China

     China

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

  • This paper mainly studies the integrability and localized wave solutions of a (2+1)- dimensional nonlinear wave equation. The bilinear form, Bäcklund transformation (BT), Lax pair and infinite conservation laws of this equation can be obtained by using Bell polynomials. The localized wave solutions including lump solutions, breather solutions and interaction solutions can be presented through Hirota’s bilinear method and the ansatz method. In addition, based on mixed lump-stripe soliton solutions and mixed rogue wave-stripe soliton solutions, the fission and fusion phenomena among the lump, the single stripe soliton and the double stripe solitons are discovered. The dynamical behaviors of these localized wave solutions are analyzed by numerical simulations. These investigated solutions can enrich the study of theory for the nonlinear localized waves and are useful for the study on interaction behaviors of nonlinear waves in nonlinear optics, shallow water and oceanography

• Referencias bibliográficas
  • 1. Singh, S., Ray, S.S.: New analytical solutions and integrability for the (2+1)-dimensional variable coefficients generalized Nizhnik-Novikov–Veselov...
  • 2. Kumar, S., Hamid, I., Abdou, M.A.: Specific wave profiles and closed-form soliton solutions for generalized nonlinear wave equation in...
  • 3. Cao, F., Lü, X., Zhou, Y.X., Cheng, X.Y.: Modified SEIAR infectious disease model for Omicron variants spread dynamics. Nonlinear Dyn....
  • 4. Zhang, Y., Lü, X.: Data-driven solutions and parameter discovery of the extended higher-order nonlinear Schrödinger equation in optical...
  • 5. Rizvi, S.T.R., Seadawy, A.R., Naqvi, S.K., Abbas, S.O.: Study of mixed derivative nonlinear Schrödinger equation for rogue and lump waves,...
  • 6. Seadawy, A.R.: Stability analysis for Zakharov–Kuznetsov equation of weakly nonlinear ion-acoustic waves in a plasma. Comput. Math. Appl....
  • 7. Ma, Y.L., Li, B.Q.: The dynamics on soliton molecules and soliton bifurcation for an extended generalization of Vakhnenko equation. Qual....
  • 8. Haque, A., Islam, M.T., Akbar, M.A., Osman, M.S.: Analysis of the propagation of nonlinear waves arise in the Heisenberg ferromagnetic...
  • 9. Sun, S.F., Tian, S.F., Li, B.: The data-driven rogue waves of the Hirota equation by using mix-training PINNs approach. Phys. D 465, 134202...
  • 10. Rizvi, S.T.R., Mustafa, B., Abbas, S.O.: Generation of optical dromions to generalized stochastic nonlinear Schrödinger equation with...
  • 11. Rizvi, S.T.R., Seadawy, A.R., Younis, M., Abbas, S.O., Khaliq, A.: Optical dromions for complex Ginzburg Landau model with nonlinear media....
  • 12. Sun, B.N., Wazwaz, A.M.: Interaction of lumps and dark solitons in the Mel’nikov equation. Nonlinear Dyn. 92, 2049–2059 (2018)
  • 13. Dullin, H.R., Gottwald, G.A., Holm, D.D.: An integrable shallow water equation with linear and nonlinear dispersion. Phys. Rev. Lett....
  • 14. Akter, R., Sarker, S., Adhikary, A., Akbar, M.A., Dey, P., Osman, M.S.: Dynamics of geometric shape solutions for space-time fractional...
  • 15. Li, W.T., Li, B.: Construction of degenerate lump solutions for (2+1)-dimensional Yu–Toda–Sasa– Fukuyama equation. Chaos Solitons...
  • 16. Zhang, Z., Yang, X.Y., Li, W.T., Li, B.: Trajectory equation of a lump before and after collision with line, lump, and breather waves...
  • 17. 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...
  • 18. Shen, Y., Tian, B., Cheng, C.D., Zhou, T.Y.: Interactions of certain localized waves for an extended (3+1)-dimensional Kadomtsev–Petviashvili...
  • 19. Shen, Y., Tian, B., Cheng, C.D., Zhou, T.Y.: N-soliton, Mth-order breather, Hth-order lump, and hybrid solutions of an extended (3+1)-dimensional...
  • 20. Wang, Y., Lü, X.: Bäcklund transformation and interaction solutions of a generalized Kadomtsev– Petviashvili equation with variable coefficients....
  • 21. Ma, Y.L., Li, B.Q.: Soliton interactions, soliton bifurcations and molecules, breather molecules, breather-to-soliton transitions, and...
  • 22. Wu, H.Y.: On Bäcklund transformations for nonlinear partial differential equations. J. Math. Anal. Appl. 192, 151–179 (1995)
  • 23. Llibre, J., Zhang, X.: On the Darboux integrability of polynomial differential systems. Qual. Theory Dyn. Syst. 11, 129–144 (2012)
  • 24. Zhou, Z.X.: Darboux transformations and global solutions for a nonlocal derivative nonlinear Schrödinger equation. Commun. Nonlinear Sci....
  • 25. Wang, D., Gao, Y.T., Yu, X., Deng, G.F., Liu, F.Y.: Painlevé analysis, Bäcklund transformation, Lax pair, periodic-and travelling-wave...
  • 26. Lü, X., Zhang, L.L., Ma, W.X.: Oceanic shallow-water description with (2+1)-dimensional generalized variablecoefficient Hirota–Satsuma–Ito...
  • 27. Zhang, L.L., Lü, X., Zhu, S.Z.: Painlevé Analysis, Bäcklund transformation and soliton solutions of the (2+1)-dimensional variable-coefficient...
  • 28. Abbas, S.O., Seadawy, A.R., Ghafoor, S., Rizvi, S.T.R.: Applications of variational integrators to couple of linear dynamical models discussing...
  • 29. Zhao, Z.L., He, L.C.: M-lump, high-order breather solutions and interaction dynamics of a generalized (2+1)-dimensional nonlinear...
  • 30. Gao, Q., Tian, S.F., Liu, J.C., Wu, Y.Q.: Breather transitions and their mechanisms of a (2+1)- dimensional Sine-Gordon equation and...
  • 31. Xu, T., Wang, D.H., Li, M., Liang, H.: Soliton and breather solutions of the Sasa–Satsuma equation via the Darboux transformation. Phys....
  • 32. Ma, W.X.: Lump solutions to the Kadomtsev–Petviashvili equation. Phys. Lett. A 379, 1975–1978 (2015)
  • 33. Ma, W.X., Zhou, Y.: Lump solutions to nonlinear partial differential equations via Hirota bilinear forms. J. Differ. Equ. 264, 2633–2659...
  • 34. Manukure, S., Zhou, Y., Ma, W.X.: Lump solutions to a (2+1)-dimensional extended KP equation. Comput. Math. Appl. 75, 2414–2419 (2018)
  • 35. Ma, Y.L., Li, B.Q.: Optical soliton resonances, soliton molecules to breathers for a defocusing Lakshmanan–Porsezian–Daniel system. Opt....
  • 36. Ma, Y.L.,Wazwaz, A.M., Li, B.Q.: Phase transition from soliton to breather, soliton-breather molecules, breather molecules of the Caudrey–Dodd–Gibbon...
  • 37. Ma, Y.L., Wazwaz, A.M., Li, B.Q.: Soliton resonances, soliton molecules, soliton oscillations and heterotypic solitons for the nonlinear...
  • 38. Seadawy, A.R., Alsaedi, B.: Contraction of variational principle and optical soliton solutions for two models of nonlinear Schrödinger...
  • 39. Seadawy, A.R., Alsaedi, B.A.: Soliton solutions of nonlinear Schrödinger dynamical equation with exotic law nonlinearity by variational...
  • 40. Raza, N., Osman, M.S., Abdel-Aty, A.H., Abdel-Khalek, S., Besbes, H.R.: Optical solitons of spacetime fractional Fokas–Lenells equation...
  • 41. Zhang, H.Q., Ma, W.X.: Lump solutions to the (2+1)-dimensional Sawada–Kotera equation. Nonlinear Dyn. 87, 2305–2310 (2017)
  • 42. Huang, L.L., Chen, Y.: Lump solutions and interaction phenomenon for (2+1)-dimensional Sawada– Kotera equation. Commun. Theor. Phys....
  • 43. Wang, C.J.: Spatiotemporal deformation of lump solution to (2+1)-dimensional KdV equation. Nonlinear Dyn. 84, 697–702 (2016)
  • 44. Wang, H., Tian, S.F., Zhang, T.T., Chen, Y., Fang, Y.: General lump solutions, lumpoff solutions, and rogue wave solutions with predictability...
  • 45. Sheng, H.H., Yu, G.F., Zhong, Y.N.: A special two-dimensional lattice by Blaszak and Szum: solitons, breathers, lump solutions, and their...
  • 46. Fan, F.C., Xu, Z.G.: Breather and rogue wave solutions for the generalized discrete Hirota equation via Darboux-Bäcklund transformation....
  • 47. Chu, J.Y., Chen, X., Liu, Y.Q.: Integrability, lump solutions, breather solutions and hybrid solutions for the (2+1)-dimensional variable...
  • 48. Chu, J.Y., Liu, Y.Q., Chen, X.: Integrability and exact solutions of the (2+1)-dimensional variable coefficient Ito equation. Nonlinear...
  • 49. Miura, R.M.: Korteweg-de Vries equation and generalizations. I. A remarkable explicit nonlinear transformation. J. Math. Phys. 9, 1202–1204...
  • 50. Hua, Y.F., Guo, B.L., Ma, W.X., Lü, X.: Interaction behavior associated with a generalized (2+1)- dimensional Hirota bilinear equation...
  • 51. Ma, Y.L., Li, B.Q.: Interaction behaviors between solitons, breathers and their hybrid forms for a short pulse equation. Qual. Theory...
  • 52. Pezzi, A., Comito, T., Bustamante,M.D., Onorato,M.: Three-and four-wave resonances in the nonlinear quadratic Kelvin lattice. Commun....
  • 53. Ren, B., Lin, J.: The integrability of a (2+1)-dimensional nonlinear wave equation: Painlevé property, multi-order breathers, multi-order...
  • 54. Pierce, A.D.: Wave equation for sound in fluids with unsteady inhomogeneous flow. J. Acoust. Soc. Am. 87, 2292–2299 (1990)
  • 55. Schäfer, T., Wayne, C.E.: Propagation of ultra-short optical pulses in cubic nonlinear media. Phys. D 196, 90–105 (2004)
  • 56. Wang, J.D., Zhang, L.J., Huo, X.W., Ma, N., Khalique, C.M.: Traveling wave solutions for two perturbed nonlinear wave equations with distributed...
  • 57. Karczewska, A., Rozmej, P., Infeld, E.: Shallow-water soliton dynamics beyond the Korteweg-de Vries equation. Phys. Rev. E 90, 012907...
  • 58. Wang, J.H., Ma, Q.W., Yan, S.Q.: A fully nonlinear numerical method for modeling wave-current interactions. J. Comput. Phys. 369, 173–190...
  • 59. Zhang, X.Q., Ren, B.: Resonance solitons, soliton molecules and hybrid solutions for a (2+1)- dimensional nonlinear wave equation...
  • 60. Zhao, X., Tian, B., Tian, H.Y., Yang, D.Y.: Bilinear Bäcklund transformation, Lax pair and interactions of nonlinear waves for a generalized...
  • 61. He, L.C., Zhang, J.W., Zhao, Z.L.: Resonance Y-type soliton, hybrid and quasi-periodic wave solutions of a generalized (2+1)-dimensional...
  • 62. Ma, W.X.: A search for lump solutions to a combined fourth-order nonlinear PDE in (2+1)-dimensions. J. Appl. Anal. Comput. 9, 1319–1332...
  • 63. Yu, J.P., Ma, W.X., Ren, B., Sun, Y.L., Khalique, C.M.: Diversity of interaction solutions of a shallow water wave equation. Complexity...
  • 64. Li, Y.H., An, H.L., Zhang, Y.Y.: Abundant fission and fusion solutions in the (2+1)-dimensional generalized Calogero–Bogoyavlenskii–Schiff...
  • 65. Wang, Y.H., Chen, Y.: Binary Bell polynomial manipulations on the integrability of a generalized (2+1)-dimensional Korteweg-de Vries...
  • 66. Singh, M., Gupta, R.K.: Bäcklund transformations, Lax system, conservation laws and multisoliton solutions for Jimbo–Miwa equation with...
  • 67. Lan, Z.Z., Gao, Y.T., Yang, J.W., Su, C.Q., Gao, Z., Zhe, G.: Solitons and Bäcklund transformation for a generalized (3+1)-dimensional...
  • 68. Wang, Y.H., Temuer, C., Yang, Y.Q.: Integrability for the generalised variable-coefficient fifth-order Korteweg-de Vries equation with...
  • 69. Fan, E.G.: The integrability of nonisospectral and variable-coefficient KdV equation with binary Bell polynomials. Phys. Lett. A 375,...
  • 70. Fan, E.G., Chow, K.W.: Darboux covariant Lax pairs and infinite conservation laws of the (2+1)- dimensional breaking soliton equation....
  • 71. Fan, E.G., Hon, Y.C.: Super extension of Bell polynomials with applications to supersymmetric equations. J. Math. Phys. 53, 013503 (2012)
  • 72. Baronio, F., Wabnitz, S., Kodama, Y.: Optical Kerr spatiotemporal dark-lump dynamics of hydrodynamic origin. Phys. Rev. Lett. 116, 173901...
  • 73. Singh, N., Stepanyants, Y.: Obliquely propagating skew KP lumps. Wave Motion 64, 92–102 (2016)
  • 74. Chen, Y.Q., Tang, Y.H., Manafian, J., Rezazadeh, H., Osman, M.S.: Dark wave, rogue wave and perturbation solutions of Ivancevic option...
  • 75. Seadawy, A.R., Arshad, M., Lu, D.C.: The weakly nonlinear wave propagation theory for the Kelvin– Helmholtz instability in magnetohydrodynamics...
  • 76. Costabile, P., Costanzo, C., Gangi, F., De Gaetani, C.I., Rossi, L., Gandolfi, C., Masseroni, D.: Highresolution 2D modelling for simulating...
  • 77. Mean, S., Unami, K., Fujihara, M.: Level-set methods applied to the kinematic wave equation governing surface water flows. J. Environ....