Ir al contenido

Documat

Novel Superposition Solutions for an Extended (3+1)-Dimensional Generalized Shallow Water Wave Equation in Fluid Mechanics and Plasma Physics

  • Peng-Fei Han [1] ; Kun Zhu [2] ; Wen-Xiu Ma [3]
    1. [1] Zhejiang Normal University

      Zhejiang Normal University

      China

    2. [2] Nanchang Normal University

      Nanchang Normal University

      China

    3. [3] University of South Florida

      University of South Florida

      Estados Unidos

    Mostrar afiliaciones +
  • Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 3, 2025
  • Idioma: inglés
  • Enlaces
  • Resumen

    • Water waves play a crucial role in elucidating fluid dynamics and plasma physics, as they significantly influence phenomena such as wave propagation, energy transfer, and stability across diverse environments. In this paper, we aim to construct the bilinear auto-Bäcklund transformation and novel function superposition solutions for an extended (3+1)-dimensional generalized shallow water wave equation by employing the Hirota bilinear method and symbolic computation. We meticulously illustrate and analyze the dynamic behavior of interactions between lump waves and two kink waves under various periodic wave backgrounds. This includes the collision of the lump wave with the two kink waves, the splitting of the kink waves, and the emergence and degeneration of the lump wave. By scrutinizing the interactions of breather waves, we observe the fusion and separation phenomena involving bell-shaped waves and breather waves. Additionally, by examining the interactions of rogue waves, we analyze their fission and fusion processes. The interplay among these waves can significantly enhance our understanding of the characteristics of solutions involving function superposition, potentially shedding light on certain physical phenomena within the realm of nonlinear science.

  • Referencias bibliográficas
    • 1. Alam, M.N., Rahman, M.A.: Study of the parametric effect of the wave profiles of the time-space fractional soliton neuron model equation...
    • 2. Bekir, A., Aksoy, E.: Exact solutions of extended shallow water wave equations by exp-function method. Int. J. Numer. Method. H. 23(2),...
    • 3. Chen, J.C., Feng, B.F., Chen, Y., Ma, Z.Y.: General bright-dark soliton solution to (2+1)-dimensional multi-component long-wave-short-wave...
    • 4. Alam, M.N.: An analytical technique to obtain traveling wave solutions to nonlinear models of fractional order. Partial Differ. Equ. Appl....
    • 5. Sulaiman, T.A., Yusuf, A., Abdeljabbar, A., Alquran, M.: Dynamics of lump collision phenomena to the (3+1)-dimensional nonlinear evolution...
    • 6. Rao, J.G., He, J.S., Cheng, Y.: The Davey-Stewartson I equation: doubly localized two-dimensional rogue lumps on the background of homoclinic...
    • 7. Ma, H.C., Mao, X., Deng, A.P.: Interaction solutions for the second extended (3+1)-dimensional JimboMiwa equation. Chinese Phys. B...
    • 8. Wang, K.L.: An efficient scheme for two different types of fractional evolution equations. Fractals 32(05), 2450093 (2024). https://doi.org/10.1142/S0218348X24500932
    • 9. Ma, Y.L., Li, B.Q.: The dynamics on soliton molecules and soliton bifurcation for an extended generalization of Vakhnenko equation. Qual....
    • 10. Wang, D., Gao, Y.T., Yu, X., Deng, G.F., Liu, F.Y.: Painlevé analysis, Bäcklund transformation, Lax pair, periodic-and travelling-wave...
    • 11. Gao, X.Y.: In plasma physics and fluid dynamics: Symbolic computation on a (2+1)-dimensional variable-coefficient Sawada-Kotera system....
    • 12. Alam, M.N., Rahim, M.A., Hossain, M.N., Tunç, C.: Dynamics of damped and undamped wave natures of the fractional Kraenkel-Manna-Merle...
    • 13. Han, P.F., Zhang, Y.: Linear superposition formula of solutions for the extended (3+1)-dimensional shallow water wave equation. Nonlinear...
    • 14. Alam, M.N., Akash, H.S., Saha, U., Hasan, M.S., Parvin, M.W., Tunç, C.: Bifurcation analysis and solitary wave analysis of the nonlinear...
    • 15. Raza, N., Jannat, N., Basendwah, G.A., Bekir, A.: Dynamical analysis and extraction of solitonic structures of a novel model in shallow...
    • 16. Ma, Y.L., Li, B.Q.: Soliton interactions, soliton bifurcations and molecules, breather molecules, breather-to-soliton transitions, and...
    • 17. Feng, C.H., Tian, B., Gao, X.T.: Bilinear form, N solitons, breathers and periodic waves for a (3+1)- dimensional Korteweg-de Vries...
    • 18. Gao, X.Y.: Hetero-Bäcklund transformation, bilinear forms and multi-solitons for a (2+1)-dimensional generalized modified dispersive...
    • 19. Sun, H.Q., Chen, A.H.: Lump and lump-kink solutions of the (3+1)-dimensional Jimbo-Miwa and two extended Jimbo-Miwa equations. Appl....
    • 20. Chen, J.C., Yan, Q.X.: Bright soliton solutions to a nonlocal nonlinear Schrödinger equation of reversetime type. Nonlinear Dyn. 100,...
    • 21. Wang, K.L.: New solitary wave solutions of the fractional modified KdV-Kadomtsev-Petviashvili equation. Fractals 31(03), 2350025 (2023)....
    • 22. Rao, J.G., Mihalache, D., Zhou, F., He, J.S., Chen, S.A.: Dark and antidark solitons on continuous and doubly periodic backgrounds in...
    • 23. Li, B.Q., Wazwaz, A.M., Ma, Y.L.: Soliton resonances, soliton molecules to breathers, semi-elastic collisions and soliton bifurcation...
    • 24. Osman, M.S.: On multi-soliton solutions for the (2+1)-dimensional breaking soliton equation with variable coefficients in a graded-index...
    • 25. Liu, J.G., Wazwaz, A.M.: Breather wave and lump-type solutions of new (3+1)-dimensional BoitiLeon-Manna-Pempinelli equation in incompressible...
    • 26. Giné, J., Sinelshchikov, D.I.: On the geometric and analytical properties of the anharmonic oscillator. Commun. Nonlinear Sci. Numer....
    • 27. Han, P.F., Bao, T.: Hybrid localized wave solutions for a generalized Calogero-BogoyavlenskiiKonopelchenko-Schiff system in a fluid or...
    • 28. Han, P.F., Zhang, Y., Jin, C.H.: Novel evolutionary behaviors of localized wave solutions and bilinear auto-Bäcklund transformations for...
    • 29. Ma, Y.L., Li, B.Q.: Phase transitions of lump wave solutions for a (2+1)-dimensional coupled Maccari system. Eur. Phys. J. Plus 139(1),...
    • 30. Ma, W.X.: Binary Darboux transformation of vector nonlocal reverse-time integrable NLS equations. Chaos Soliton. Fract. 180, 114539 (2024)....
    • 31. Zhao, H.Q., Ma, W.X.: Mixed lump-kink solutions to the KP equation. Comput. Math. Appl. 74(6), 1399–1405 (2017). https://doi.org/10.1016/j.camwa.2017.06.034
    • 32. Ma, W.X., Yong, X.L., Zhang, H.Q.: Diversity of interaction solutions to the (2+1)-dimensional Ito equation. Comput. Math. Appl. 75(1),...
    • 33. Ünsal, Ö., Bekir, A., Ta¸scan, F., Naci Özer, M.: Complexiton solutions for two nonlinear partial differential equations via modification...
    • 34. Alhami, R., Alquran, M.: Extracted different types of optical lumps and breathers to the new generalized stochastic potential-KdV equation...
    • 35. Ma, H.C., Chen, X.Y., Deng, A.P.: Novel soliton molecule solutions for the second extend (3+1)- dimensional Jimbo-Miwa equation in...
    • 36. Han, P.F., Ye, R.S., Zhang, Y.: Inverse scattering transform for the coupled Lakshmanan-PorsezianDaniel equations with non-zero boundary...
    • 37. Han, P.F., Ma, W.X., Ye, R.S., Zhang, Y.: Inverse scattering transform for the defocusing-defocusing coupled Hirota equations with non-zero...
    • 38. Zhang, X.F., Tian, S.F., Yang, J.J.: The Riemann-Hilbert approach for the focusing Hirota equation with single and double poles. Anal....
    • 39. Gao, X.Y.: In the shallow water: Auto-Bäcklund, hetero-Bäcklund and scaling transformations via a (2+1)-dimensional generalized Broer-Kaup...
    • 40. Jiwari, R., Kumar, V., Singh, S.: Lie group analysis, exact solutions and conservation laws to compressible isentropic Navier-Stokes equation....
    • 41. Ma, H.C.: A simple method to generate Lie point symmetry groups of the (3+1)-dimensional JimboMiwa equation. Chinese Phys. Lett. 22(3),...
    • 42. Wang, K.L.: New analysis methods for the coupled fractional nonlinear Hirota equation. Fractals 31(09), 2350119 (2023). https://doi.org/10.1142/S0218348X23501190
    • 43. Alam, M.N.: Soliton solutions to the electric signals in telegraph lines on the basis of the tunnel diode. Partial Differ. Equ. Appl....
    • 44. Zhao, N., Chen, Y.H., Cheng, L., Chen, J.C.: Data-driven soliton solutions and parameter identification of the nonlocal nonlinear Schrödinger...
    • 45. Iqbal, M., Alam, M.N., Lu, D.C., Seadawy, A.R., Alsubaie, N.E., Ibrahim, S.: On the exploration of dynamical optical solitons to the modify...
    • 46. Han, P.F., Zhang, Y.: Investigation of shallow water waves near the coast or in lake environments via the KdV-Calogero-Bogoyavlenskii-Schiff...
    • 47. Yang, X.L., Zhang, Y., Li, W.J.: Dynamics of general soliton and rational solutions in the (3+1)- dimensional nonlocal Mel’nikov equation...
    • 48. Alam, M.N., Alp ˙Ilhan, O., Akash, H.S., Talib, I.: Bifurcation analysis and new exact complex solutions for the nonlinear Schrödinger...
    • 49. Yang, J.Y., Ma, W.X.: Abundant interaction solutions of the KP equation. Nonlinear Dyn. 89, 1539– 1544 (2017). https://doi.org/10.1007/s11071-017-3533-y
    • 50. Alam, M.N., Talib, I., Tunç, C.: The new soliton configurations of the 3D fractional model in arising shallow water waves. Int. J. Appl....
    • 51. Gao, X.Y.: Auto-Bäcklund transformation with the solitons and similarity reductions for a generalized nonlinear shallow water wave equation....
    • 52. Cheng, L., Zhang, Y., Ma, W.X., Hu, Y.W.: Wronskian rational solutions to the generalized (2+1)- dimensional Date-Jimbo-Kashiwara-Miwa...
    • 53. Tariq, K.U., Bekir, A., Ilyas, H.: Solitons, lumps, breathers and rouge wave solutions to the (3+1)- dimensional generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt...
    • 54. Clarkson, P.A., Mansfield, E.L.: On a shallow water wave equation. Nonlinearity 7(3), 975 (1994). https://doi.org/10.1088/0951-7715/7/3/012
    • 55. Dullin, H.R., Gottwald, G.A., Holm, D.D.: On asymptotically equivalent shallow water wave equations. Physica D 190(1–2), 1–14 (2004)....
    • 56. Thacker, W.C.: Some exact solutions to the nonlinear shallow-water wave equations. J. Fluid Mech. 107, 499–508 (1981). https://doi.org/10.1017/S0022112081001882
    • 57. Horikis, T.P., Frantzeskakis, D.J., Smyth, N.F.: Extended shallow water wave equations. Wave Motion 112, 102934 (2022). https://doi.org/10.1016/j.wavemoti.2022.102934
    • 58. Camassa, R., Huang, J.F., Lee, L.: Integral and integrable algorithms for a nonlinear shallow-water wave equation. J. Comput. Phys. 216(2),...
    • 59. Xin, Z.P., Zhang, P.: On the weak solutions to a shallow water equation. Commun. Pur. Appl. Math. 53(11), 1411–1433 (2000). DOI: https://doi.org/10.1002/1097-0312(200011)53:11<1411::AIDCPA4>3.0.CO;2-5
    • 60. Dullin, H.R., Gottwald, G.A., Holm, D.D.: An integrable shallow water equation with linear and nonlinear dispersion. Phys. Rev. Lett....
    • 61. He, L.C., Zhang, J.W., Zhao, Z.L.: M-lump and interaction solutions of a (2+1)-dimensional extended shallow water wave equation. Eur....
    • 62. Tang, Y.N., Zai, W.J.: New periodic-wave solutions for (2+1)- and (3+1)-dimensional Boiti-LeonManna-Pempinelli equations. Nonlinear...
    • 63. Liu, J.G., He, Y.: New periodic solitary wave solutions for the (3+1)-dimensional generalized shallow water equation. Nonlinear Dyn....
    • 64. Ma, W.X.: Lump-type solutions to the (3+1)-dimensional Jimbo-Miwa equation. Int. J. Nonlinear Sci. Numer. 17, 355–359 (2016). https://doi.org/10.1515/ijnsns-2015-0050
    • 65. Ma, H.C., Huang, H.Y., Deng, A.P.: Soliton molecules and some interaction solutions for the (3+1)- dimensional Jimbo-Miwa equation....
    • 66. Ismael, H.F., El-Ganaini, S., Bulut, H.:M-lump waves and their interactions with multi-soliton solutions for the (3+1)-dimensional...
    • 67. Alquran, M., Alhami, R.: Analysis of lumps, single-stripe, breather-wave, and two-wave solutions to the generalized perturbed-KdV equation...
    • 68. Gao, X.Y.: Oceanic shallow-water investigations on a generalized Whitham-Broer-Kaup-BoussinesqKupershmidt system. Phys. Fluids. 35, 127106...
    • 69. Liu, J.G., Zhu, W.H., Osman, M.S., Ma, W.X.: An explicit plethora of different classes of interactive lump solutions for an extension...
    • 70. Wazwaz, A.M., El-Tantawy, S.A.: Solving the (3+1)-dimensional KP-Boussinesq and BKP-Boussinesq equations by the simplified Hirota’s...
    • 71. Shen, Y., Tian, B.: Bilinear auto-Bäcklund transformations and soliton solutions of a (3+1)-dimensional generalized nonlinear evolution...
    • 72. Gao, X.Y.: Symbolic computation on a (2+1)-dimensional generalized nonlinear evolution system in fluid dynamics, plasma physics, nonlinear...
    • 73. Ji, Y., Tan,W.: New soliton solutions and trajectory equations of soliton collision to a (2+1)-dimensional shallow water wave model....
    • 74. Guo, Y.F., Guo, C.X., Li, D.L.: The lump solutions for the (2+1)-dimensional Nizhnik-Novikov-Veselov equations. Appl. Math. Lett....
    • 75. Hirota, R.: The Direct Method in Soliton Theory. Cambridge University Press, New York (2004)
    • 76. Rao, J.G., Mihalache, D., He, J.S.: Multiple solitons and breathers on periodic backgrounds in the complex modified Korteweg-de Vries...
    • 77. Wang, K.L.: New computational approaches to the fractional coupled nonlinear Helmholtz equation. Eng. Computation. 41(5), 1285–1300 (2024)....
    • 78. Chen, J.C., Feng, B.F.: Tau-function formulation for bright, dark soliton and breather solutions to the massive Thirring model. Stud....
    • 79. Ma, H.C., Qi, X.R., Deng, A.P.: Soliton solutions and the interaction behaviour of the (3+1)-dimensional Jimbo-Miwa-like equation....
    • 80. Kumar, D., Raju, I., Paul, G.C., Ali, M.E., Haque, M.D.: Characteristics of lump-kink and their fissionfusion interactions, rogue, and...
    • 81. Yang, J.J., Tian, S.F., Peng, W.Q., Li, Z.Q., Zhang, T.T.: The lump, lumpoff and rouge wave solutions of a (3+1)-dimensional generalized...
    • 82. Ismael, H.F., Seadawy, A., Bulut, H.: Multiple soliton, fusion, breather, lump, mixed kink-lump and periodic solutions to the extended...
    • 83. Han, P.F., Zhang, Y.: Superposition behavior of the lump solutions and multiple mixed function solutions for the (3+1)-dimensional...
    • 84. Chen, J.C., Yang, B., Feng, B.F.: Rogue waves in the massive Thirring model. Stud. Appl. Math. 151(3), 1020–1052 (2023). https://doi.org/10.1111/sapm.12619
    • 85. Wang, K.L., Wei, C.F.: Novel optical soliton solutions of the fractional perturbed Schrödinger equation in optical fiber. Fractals in...
    • 86. Alam, M.N., Iqbal, M., Hassan, M., Fayz-Al-Asad, M., Hossain, M.S., Tunç, C.: Bifurcation, phase plane analysis and exact soliton solutions...
    • 87. Mandal, U.K., Das, A., Ma, W.X.: Integrability, breather, rogue wave, lump, lump-multi-stripe, and lump-multi-soliton solutions of a (3+1)-dimensional...
Fundación Dialnet

Mi Documat

Opciones de artículo

Opciones de compartir

Opciones de entorno