The Nonlocal (2+1)-Dimensional ABKP System: Hirota Analysis, Soliton Dynamics and Novel Wave Structures

• Litao Gai ^[1] ; Wenyu Wu ^[1] ; Runfa Zhang ^[2]
  1. [1] Zhejiang Normal University

     Zhejiang Normal University

     China

     
  2. [2] Shanxi University

     Shanxi University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 25, Nº 3, 2026
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • Nonlocal integrable nonlinear systems can be used to excite some novel nonlinear phenomena when considering the nonlocal conditions and interactions of fluids.Revealing the dynamic behaviors of shallow-water waves in the ocean, the nonlocal ABKP system in (2+1)-dimensions will be considered in this article. Firstly, the Hirota method is used to establish a standard condition of n-solitons, based on the bilinear equation of Bell’s polynomial theory. Particularly, a series of analyses are conducted on the Hirota condition, resulting in novel wave structures including multi-breather, multilump and lump-breather waves. Furthermore, the stability analysis for ABKP system is discussed using the qualitative theory, and a solitary wave solution is presented via Hamilton potential function. Finally, two novel types of exact network model solutions are derived via bilinear neural network approach. All 3-D and 2-D plots effectively illustrate the wave characteristics for the solutions obtained. The methods employed of this study are effective for analyzing the nonlinear dynamics of nonlocal integrable systems. Meanwhile, the results obtained are helpful for further deepening the understanding of nonlinear phenomena in fluid physics or plasma physics.

• Referencias bibliográficas
  • 1. Ablowitz, M.J., Musslimani, Z.H.: Integrable nonlocal nonlinear Schrödinger equation. Phys. Rev. Lett. 110, 064105 (2013)
  • 2. Ma, W.X.: Inverse scattering for nonlocal reverse-time nonlinear Schrödinger equations. Appl. Math. Lett. 102, 106161 (2020)
  • 3. Ma, W.X.: Inverse scattering and soliton solutions of nonlocal complex reverse-spacetime mKdV equations. J. Geom. Phys. 157, 103845 (2020)
  • 4. Zhang, G.Q., Yan, Z.Y., Chen, Y.: Novel higher-order rational solitons and dynamics of the defocusing integrable nonlocal nonlinear Schrödinger...
  • 5. Yang, B., Chen, Y.: Reductions of Darboux transformations for the PT-symmetric nonlocal Davey- Stewartson equations. Appl. Math. Lett....
  • 6. Yang, B.,Chen,Y.:Dynamics of roguewaves in the partially PT-symmetric nonlocal Davey-Stewartson systems. Commun. Nonlinear Sci. Numer....
  • 7. Xu, C.X., Xu, T., Meng, D.X., et al.: Binary Darboux transformation and new soliton solutions of the focusing nonlocal nonlinear Schrödinger...
  • 8. Li, L.,Wang, L.,Yu, F.J.: Some general bright soliton solutions and interactions for a (2+1)-dimensional nonlocal nonlinear Schrödinger...
  • 9. Wang, X.B., Tian, S.F.: Exotic vector freak waves in the nonlocal nonlinear Schrödinger equation. Phys. D 442, 133528 (2022)
  • 10. Yang, Y.M., Xia, T.C., Liu, T.S.: Darboux transformation and exact solution to the nonlocal Kundu- Eckhaus equation. Appl. Math. Lett....
  • 11. Yang, Y.L., Fan, E.G.: Riemann-Hilbert approach to the modified nonlinear Schrödinger equation with non-vanishing asymptotic boundary...
  • 12. Ma,W.X.: Riemann-Hilbert problems and soliton solutions of nonlocal real reverse-spacetime mKdV equations. J. Math. Anal. Appl. 498, 124980...
  • 13. Chen, M.S., Fan, E.G.: Riemann-Hilbert approach for discrete sine-Gordon equation with simple and double poles. Stud. Appl. Math. 148,...
  • 14. Peng, W.Q., Chen, Y.: N-double poles solutions for nonlocal Hirota equation with nonzero boundary conditions using Riemann-Hilbert method...
  • 15. Ma, W.X.: Type (-λ, -λ ∗) reduced nonlocal integrable mKdV equations and their soliton solutions. Appl. Math. Lett. 131, 108074 (2022)
  • 16. Ma,W.X.: Riemann-Hilbert problems and inverse scattering of nonlocal real reverse-spacetime matrix AKNS hierarchies. Phys. D 430, 133078...
  • 17. Rao, J.G., Cheng, Y., Porsezian, K., et al.: PT-symmetric nonlocal Davey-Stew-artson I equation: Soliton solutions with nonzero background....
  • 18. Zhao, N., Cheng, L., Chen, J.C., et al.: Bright soliton solutions to the nonlocal Manakov equations of reverse-space type. Appl. Math....
  • 19. Luo, J.H., Fan, E.G.: ¯∂-dressing method for the nonlocal mKdV equation. J. Geom. Phys. 177, 104550 (2022)
  • 20. Zhou, X., Fan, E.G.: Long time asymptotics for the nonlocal mKdV equation with finite density initial data. Phys. D 440, 133458 (2022)
  • 21. Wu, H.X., Zeng, Y.B., Fan, T.Y.: Soliton, positon and negaton solutions of extended KdV equation. Commun. Theor. Phys. 49, 529–534 (2008)
  • 22. Mo, J.Q.: Soliton, generalized variational iteration solution of soliton for disturbed KdV equation. Commun. Theor. Phys. 53, 440–442...
  • 23. Zhao, Z.L., He, L.C.: Space-curved resonant solitons and inelastic interaction solutions of a (2+1)- dimensional generalized KdV equation....
  • 24. Wu, G.Z., Dai, C.Q.: Nonautonomous soliton solutions of variable-coefficient fractional nonlinear Schrödinger equation. Appl. Math. Lett....
  • 25. Han, H.B., Li, H.J., Dai, C.Q.: Wick-type stochastic multi-soliton and soliton molecule solutions in the framework of nonlinear Schrödinger...
  • 26. Sang, X., Dong, H.H., Fang, Y., et al.: Soliton, breather and rogue wave solutions of the nonlinear Schrödinger equation via Darboux transformation...
  • 27. Zhang, D.J., Chen, D.Y.: The N-soliton solutions of the sine-Gordon equation with self-consistent sources. Phys. A 321, 467–481 (2003)
  • 28. Zhang, M.H.,Weng,W.F., Yan, Z.Y.: Interactions of fractional N-solitons with anomalous dispersions for the integrable combined fractional...
  • 29. Li, Z.Q., Tian, S.F., Yang, J.J.: On the asymptotic stability of N-soliton solution for the short pulse equation with weighted Sobolev...
  • 30. Wei, J.,Wang, J.Y., Li,Y.H.: Soliton and breather solutions of a reverse time nonlocal coupled nonlinear Schrödinger equation with four-wave...
  • 31. Lou, S.Y.: Alice-Bob systems, P-T-C symmetry invariant and symmetry breaking soliton solutions. J. Math. Phys. 59, 083507 (2018)
  • 32. Cao, Y.L., He, J.S., Cheng, Y.: The partial-rogue ripple solutions of nonlocal Kadomtsev-Petviashvili equation. Phys. D 458, 133990 (2024)
  • 33. Lou, S.Y.: Prohibitions caused by nonlocality for nonlocal Boussinesq-KdV type systems. Stud. Appl. Math. 143, 123–138 (2019)
  • 34. Zhao, Q.L., Lou, S.Y., Jia, M.: Solitons and soliton molecules in two nonlocal Alice-Bob Sawada- Kotera systems. Commun. Theor. Phys....
  • 35. Lou, S.Y.: Multi-place physics and multi-place nonlocal systems. Commun. Theor. Phys. 72, 057001 (2020)
  • 36. Wu, H.Y., Fei, J.X., Ma, Z.Y., et al.: Symmetry breaking soliton, breather, and lump solutions of a nonlocal Kadomtsev-Petviashvili system....
  • 37. Dong, P., Ma, Z.Y., Wu, H.L., et al.: The symmetry breaking solutions of the nonlocal Alice-Bob B-type Kadomtsev-Petviashvili system....
  • 38. Feng, Y.Y., Sudao, B.: Multi-breather, multi-lump and hybrid solutions to a novel KP-like equation. Nonlinear Dyn. 106, 879–890 (2021)
  • 39. Han, T., Jiang, Y., Fan, H.: Exploring shallow water wave phenomena: a fractional approach to the Whitham-Broer-Kaup-Boussinesq-Kupershmidt...
  • 40. Kumar, S., Rani, S., Ma, W.X.: Lie symmetries, modulation instability, conservation laws, and the dynamic waveform patterns of several...
  • 41. Ahmed, S., Aldawish, I., Rizvi, S.T.R., et al.: Iterative investigation of the nonlinear fractional Cahn- Allen and fractional clannish...
  • 42. Kukkar, A.,Kumar, S.: Dynamic behavior of dark and bright solitons with analytical solutions, together with other soliton forms in the...
  • 43. Kumar, S., Kukkar, A.: Dynamics of several optical soliton solutions of a (3+1)-dimensional nonlinear Schrödinger equation with parabolic...
  • 44. Kumar, S., Dhiman, S.K.: Dynamics of various solitonic formations and other solitons of a (4+1)- dimensional Davey-Stewartson-Kadomtsev-Petviashvili...
  • 45. Ouahid, L., Abdou, M.A., Kumar, S., et al.: A plentiful supply of soliton solutions for DNA Peyrard- Bishop equation by means of a new...
  • 46. Kumar, S., Dhiman, S.K.: Exploring cone-shaped solitons, breather, and lump-forms solutions using the Lie symmetry method and unified...
  • 47. Kumar, A., Kumar, S.: Dynamical behaviors with various exact solutions to a (2+1)-dimensional asymmetric Nizhnik-Novikov-Veselov equation...
  • 48. Hamid, I.,Kumar, S.: Newly formed solitarywave solutions and other solitons to the (3+1)-dimensional mKdV-ZK equation utilizing a...
  • 49. Seadawy, R., Ali, A., Radwan, T., et al.: Solitary wave solutions for the conformable time-fractional coupled Konno-Oono model via applications...
  • 50. Mehanna, M.S., Alazman, I., Seadawy, A.R.: Comprehensive study of a (3+1)-dimensional nonlinear Vakhnenko-Parkes dynamical equation...
  • 51. Kumar, S., Rani, S.: Study of exact analytical solutions and various wave profiles of a new extended (2+1)-dimensional Boussinesq...
  • 52. Kumar, S., Rani, S.: Newly constructed closed-form soliton solutions, conservation laws and modulation instability for a (2+1)-dimensional...
  • 53. Ma, W.X.: N-soliton solutions and the Hirota conditions in (2+1)-dimensions. Opt. Quant. Ele. 52, 511 (2020)
  • 54. 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...
  • 55. Ma,W.X.: N-soliton solutions and the Hirota conditions in (1+1)-dimensions. Int. J. Nonlin. Sci. Num. Simu. 23, 123–133 (2022)
  • 56. Gai, L.T., Xu, M.H., Zhang, R.F.: N-solitons, lump-stripe solitons with inelastic collisions and new periodic rogue waves of a (2+1)-dimensional...
  • 57. Kumar, S., Mohan, B.: A direct symbolic computation of center-controlled rogue waves to a new Painlevé-integrable (3+1)-D generalized...
  • 58. Mohan, B., Kumar, S.: Generalization and analytic exploration of soliton solutions for nonlinear evolution equations via a novel symbolic...
  • 59. Mohan, B., Kumar, S.: Rogue-wave structures for a generalized (3+1)-dimensional nonlinear wave equation in liquid with gas bubbles....
  • 60. Mohan, B.,Kumar, S.,Kumar, R.:On investigation of kink-solitons and roguewaves to a newintegrable (3+1)-dimensional KdV-type generalized...
  • 61. Mohan, B., Kumar, S.: Painlevé analysis, restricted bright-dark N-solitons, and N-rogue waves of a (4+1)-dimensional variable-coefficient...
  • 62. Wang, J., Li, Z.: The impact of standard Wiener process on the qualitative analysis and traveling wave solutions of stochastic nonlinear...
  • 63. Roshid,M., Ullah,M., Uddin, M., et al.:Exploring exact travelingwave solutions of fractional nonlinear model emerging from surface water...
  • 64. Raza, A., Alazman, I., Rizvi, S.T.R., et al.: Mathematical modeling and symmetry analysis of the impact of vaccination on the dynamics...
  • 65. Kumar, S., Rani, S., Mann, N.: Analytical soliton solutions to a (2+1)-dimensional variable coefficients graphene sheets equation...
  • 66. Tariq, K.U., Manafian, J., Malmir, S., et al.: On the structure of the higher dimensional Date-Jimbo- Kashiwara-Miwa model emerging in...
  • 67. Zhu, H., Manafian, J., Hammadi, A.H., et al.: Conservation law, Chupin Liu’s theorem and propagation of pulses in optical metamaterials...
  • 68. Xu, Y., Manafian, J., Ilhan, O.A., et al.: Conservation law, stability analysis, degenerate lump and traveling wave solutions for (2+1)-dimensional...
  • 69. Zhang, R.F., Li, M.C., Gan, J.Y., et al.: Novel trial functions and rogue waves of generalized breaking soliton equation via bilinear...
  • 70. Gai, L.T., Qian, Y.H., Qin, Y.P., et al.: Periodic bright-dark soliton, breather-like wave and rogue wave solutions to a ¯ p-GBS equation...
  • 71. Cao, N., Yin, X.J., Bai, S.T., et al.: Breather wave, lump type and interaction solutions for a high dimensional evolution model. Chaos...
  • 72. Gai, L.T.,Wu,W.Y., Ding, T.F., et al.: Lump wave solutions, lump-stripe soliton inelastic collision phenomena and rogue-type wave solutions...
  • 73. Xia, N., Zhang, R.F., Luo, X.F.: Three types of exact solutions of generalized breaking soliton equation via certain neural network structures....
  • 74. Naqvi, S.K., Aldawish, I., Rizvi, S.T.R., et al.: Bilinear neural network solutions for nonlinear waves in the Sawada-Kotera model studied...
  • 75. Zhou, P.,Manafian, J., Lakestani, M., et al.: Analytical evaluations using neural network-basedmethod for wave solutions of combined Kairat-II-X...
  • 76. Ma,W.X.: Bilinear equations, Bell polynomials and linear superposition principle. J. Phys: Conf. Ser. 411, 012021 (2013)
  • 77. Qian,Y., Manafian, J.,Mohyaldeen, S.Y., et al.:Multiple-order line roguewave, lumpand its interaction, periodic, and cross-kink solutions...
  • 78. Zhang, M., Xie, X., Manafian, J., et al.: Characteristics of the new multiple rogue wave solutions to the fractional generalized CBS-BK...
  • 79. Mohan, B., Kumar, S., Kumar, R.: Higher-order rogue waves and dispersive solitons of a novel P-type (3+1)-D evolution equation in...
  • 80. Guo, S., Kong, D., Manafian, J., et al.: Modulational stability and multiple rogue wave solutions for a generalized (3+1)-D nonlinear...
  • 81. Ma, W.X.: Trilinear equations, Bell polynomials, and resonant solutions. Front. Math. Chin. 8, 1139– 1156 (2013)