Lie Group Analysis for a (2+1)-dimensional Generalized Modified Dispersive Water-Wave System for the Shallow Water Waves

• Autores: Fei-Yan Liu, Yi-Tian Gao, Xin Yu, Cui-Cui Ding, Liu-Qing Li
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 22, Nº 4, 2023
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • Shallow water waves refer to the waves with the bottom boundary affecting the movement of water quality points when the ratio of water depth to wavelength is small.

    Under investigation in this paper is a (2+1)-dimensional generalized modified dispersive water-wave (GMDWW) system for the shallow water waves. We obtain the Lie point symmetry generators and Lie symmetry groups for the GMDWW system via the Lie group method. Optimal system of the one-dimensional subalgebras is derived.

    According to that optimal system, we obtain certain symmetry reductions. Hyperbolicfunction, trigonometric-function and rational solutions for the GMDWW system are derived via the polynomial expansion, Riccati equation expansion and G G expansion methods.

• Referencias bibliográficas
  • 1. Cheng, C.D., Tian, B., Ma, Y.X., et al.: Pfaffian, breather and hybrid solutions for a (2+1)-dimensional generalized nonlinear system...
  • 2. Tamang, J., Saha, A.: Bifurcations of small-amplitude supernonlinear waves of the mKdV and modified Gardner equations in a three-component...
  • 3. Moleleki, L.D., Simbanefayi, I., Khalique, C.M.: Symmetry solutions and conservation laws of a (3+1)-dimensional generalized KP-Boussinesq...
  • 4. Liu, R.X., Tian, B., Liu, L.C., et al.: Bilinear forms, N-soliton solutions and soliton interactions for a fourth-order dispersive nonlinear...
  • 5. Kayum, M.A., Ara, S., Osman, M.S., et al.: Onset of the broad-ranging general stable soliton solutions of nonlinear equations in physics...
  • 6. Yang, D.Y., Tian, B., Tian, H.Y., et al.: Darboux transformation, localized waves and conservation laws for an M-coupled variable-coefficient...
  • 7. Khalique, C.M., Adeyemo, O.D.: Langrangian formulation and solitary wave solutions of a generalized Zakharov-Kuznetsov equation with dual...
  • 8. Adeyemo, O.D.: Applications of cnoidal and snoidal wave solutions via optimal system of subalgebras for a generalized extended (2+1)-D...
  • 9. Wang, L., Gao, Y.T., Gai, X.L., et al.: Inelastic interactions and double Wronskian solutions for the Whitham-Broer-Kaup model in shallow...
  • 10. Meng, D.X., Gao, Y.T., Wang, L., et al.: Elastic and inelastic interactions of solitons for a variable coefficient generalized dispersive...
  • 11. Gao, X.T., Tian, B., Shen, Y., et al.: Considering the shallow water of a wide channel or an open sea through a generalized (2+1)-dimensional...
  • 12. Lakestani, M., Manafian, J.: Application of the ITEM for the modified dispersive water-wave system. Opt. Quantum Electron. 49, 128 (2017)
  • 13. Wang, P., Tian, B., Liu, W.J., et al.: Lax pair, Bäcklund transformation and multi-soliton solutions for the Boussinesq-Burgers equations...
  • 14. Abloeitz, M.J.: Nonlinear Dispersive Waves: Asymptotic Analysis and Solitons. Cambridge Univ. Press, Cambridge (2011)
  • 15. Zdyrski, T., Feddersen, F.: Wind-induced changes to surface gravity wave shape in shallow water. J. Fluid Mech. 913, A27 (2021)
  • 16. Liu, F.Y., Gao, Y.T., Yu, X., et al.: Wronskian, Gramian, Pfaffian and periodic-wave solutions for a (3+1)-dimensional generalized...
  • 17. Gao, X.T., Tian, B.: Water-wave studies on a (2+1)-dimensional generalized variable-coefficient BoitiLeon-Pempinelli system. Appl....
  • 18. Cheng, C.D., Tian, B., Zhou, T.Y., et al.: Wronskian solutions and Pfaffianization for a (3+1)- dimensional generalized variable-coefficient...
  • 19. Gao, X.Y., Guo, Y.J., Shan, W.R.: Shallow-water investigations: Bilinear auto-Bäcklund transformations for a (3+1)-dimensional generalized...
  • 20. Shen, Y., Tian, B., Cheng, C.D., et al.: Pfaffian solutions and nonlinear waves of a (3+1)-dimensional generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt...
  • 21. Gao, X.T., Tian, B., Feng, C.H.: In oceanography, acoustics and hydrodynamics: investigations on an extended coupled (2+1)-dimensional...
  • 22. Liu, F.Y., Gao, Y.T., Yu, X.: Rogue-wave, rational and semi-rational solutions for a generalized (3+1)- dimensional Yu-Toda-Sasa-Fukuyama...
  • 23. Chakraverty, S., Karunakar, P., Karunakar, P., et al.: Homotopy perturbation method for predicting tsunami wave propagation with crisp...
  • 24. Shen, Y., Tian, B., Liu, S.H., et al.: Studies on certain bilinear form, N-soliton, higher-order breather, periodic-wave and hybrid solutions...
  • 25. Chakravarty, S., Kodama, Y.: Construction of KP solitons from wave patterns. J. Phys. A Math. Theor. 47, 025201 (2013)
  • 26. Zabusky, N.J., Galvin, C.J.: Shallow-water waves, the Korteweg-deVries equation and solitons. J. Fluid Mech. 47, 811–824 (1971)
  • 27. Wu, H.Y., Jiang, L.H.: Instruction on the construction of coherent structures based on variable separation solutions of (2+1)-dimensional...
  • 28. Dai, C.Q., Wang, Y.Y., Biswas, A.: Dynamics of dispersive long waves in fluids. Ocean Eng. 81, 77–88 (2014)
  • 29. Tang, X.Y., Lou, S.Y., Zhang, Y.: Localized excitations in (2+1)-dimensional systems. Phys. Rev. E 66, 046601 (2002)
  • 30. Wang, M., Tian, B., Zhou, T.Y.: Darboux transformation, generalized Darboux transformation and vector breathers for a matrix Lakshmanan-Porsezian-Daniel...
  • 31. Feng, L.L., Tian, S.F., Wang, X.B., et al.: Rogue waves, homoclinic breather waves and soliton waves for the (2+1)-dimensional B-type...
  • 32. Zhou, T.Y., Tian, B., Chen, Y.Q., et al.: Painlevé analysis, auto-Bäcklund transformation and analytic solutions of a (2+1)-dimensional...
  • 33. Gao, X.Y., Guo, Y.J., Shan, W.R.: Reflecting upon some electromagnetic waves in a ferromagnetic film via a variable-coefficient modified...
  • 34. Ma, Y.L., Wazwaz, A.M., Li, B.Q.: New extended Kadomtsev-Petviashvili equation: multiple soliton solutions, breather, lump and interaction...
  • 35. Wu, X.H., Gao, Y.T., Yu, X., et al.: Binary Darboux transformation, solitons, periodic waves and modulation instability for a nonlocal...
  • 36. Zhou, T.Y., Tian, B.: Auto-Bäcklund transformations, Lax pair, bilinear forms and bright solitons for an extended (3+1)-dimensional...
  • 37. Shen, Y., Tian, B., Zhou, T.Y., et al.: N-fold Darboux transformation and solitonic interactions for the Kraenkel-Manna-Merle system in...
  • 38. Wu, X.H., Gao, Y.T., Yu, X., et al.: Vector breathers, rogue and breather-rogue waves for a coupled mixed derivative nonlinear Schrödinger...
  • 39. Zhou, T.Y., Tian, B., Zhang, C.R., et al.: Auto-Bäcklund transformations, bilinear forms, multiplesoliton, quasi-soliton and hybrid solutions...
  • 40. Yang, D.Y., Tian, B., Hu, C.C., et al.: The generalized Darboux transformation and higher-order rogue waves for a coupled nonlinear Schrödinger...
  • 41. Alam, M.N., Li, X.: Symbolic methods to construct a cusp, breathers, kink, rogue waves and some soliton waves solutions of nonlinear partial...
  • 42. Yue, C., Lu, D.C., Khater, M.M.A.: Abundant wave accurate analytical solutions of the fractional nonlinear Hirota-Satsuma-Shallow water...
  • 43. Li, L.Q., Gao, Y.T., Yu, X., et al.: Gramian solutions and solitonic interactions of a (2+1)-dimensional Broer-Kaup-Kupershmidt system...
  • 44. Abd-el-Malek, M.B., Amin, A.M.: Lie group method for solving generalized Hirota-Satsuma coupled Korteweg-de Vries (KdV) equations. Appl....
  • 45. Wu, X.H., Gao, Y.T., Yu, X., et al.: N-fold generalized Darboux transformation and soliton interactions for a three-wave resonant interaction...
  • 46. Yang, D.Y., Tian, B., Hu, C.C., et al.: Conservation laws and breather-to-soliton transition for a variablecoefficient modified Hirota...
  • 47. Adeyemo, O.D., Zhang, L., Khalique, C.M.: Bifurcation theory, Lie group-invariant solutions of subalgebras and conservation laws of a...
  • 48. Adeyemo, O.D., Khalique, C.M., Gasimov, Y.S., et al.: Variational and nonvariational approaches with Lie algebra of a generalized (3+1)-dimensional...
  • 49. Adeyemo, O.D., Khalique, C.M.: Lie group classification of generalized variable coefficient Kortewegde Vries equation with dual power-law...
  • 50. Adeyemo, O.D., Khalique, C.M.: Dynamical soliton wave structures of one-dimensional Lie subalgebras via group-invariant solutions of a...
  • 51. Adeyemo, O.D., Zhang, L., Khalique, C.M.: Optimal solutions of Lie subalgebra, dynamical system, travelling wave solutions and conserved...
  • 52. Adeyemo, O.D., Khalique, C.M.: Dynamics of soliton waves of group-invariant solutions through optimal system of an extended KP-like equation...
  • 53. Kumar, S., Rani, S.: Lie symmetry reductions and dynamics of soliton solutions of (2+1)-dimensional Pavlov equation. Pramana-J. Phys....
  • 54. Kumar, S., Rani, S.: Symmetries of optimal system, various closed-form solutions, and propagation of different wave profiles for the Boussinesq-Burgers...
  • 55. Kumar, S., Rani, S.: Study of exact analytical solutions and various wave profiles of a new extended (2+1)-dimensional Boussinesq...
  • 56. Rani, S., Kumar, S., Kumar, R.: Invariance analysis for determining the closed-form solutions, optimal system, and various wave profiles...
  • 57. Kumar, S., Rani, S.: Invariance analysis, optimal system, closed-form solutions and dynamical wave structures of a (2+1)-dimensional...
  • 58. Kumar, S., Rani, S., Mann, N.: Diverse analytical wave solutions and dynamical behaviors of the new (2+1)-dimensional Sakovich equation...
  • 59. Sahoo, S., Ray, S.S.: Lie symmetry analysis and exact solutions of (3+1) dimensional Yu-Toda-SasaFukuyama equation in mathematical...
  • 60. Hu, X., Li, Y., Chen, Y.: A direct algorithm of one-dimensional optimal system for the group invariant solutions. J. Math. Phys. 56, 053504...
  • 61. Ma, Z.Y., Fei, J.X., Du, X.Y.: Symmetry reduction of the (2+1)-dimensional modified dispersive water-wave system. Commun. Theor. Phys....
  • 62. Li, D.S., Zhang, H.Q.: New families of non-travelling wave solutions to the (2+1)-dimensional modified dispersive water-wave system....
  • 63. Liang, J.F., Wang, X.: Consistent Riccati expansion for finding interaction solutions of (2+1)- dimensional modified dispersive water-wave...
  • 64. Ren, B., Ma, W.X., Yu, J.: Rational solutions and their interaction solutions of the (2+1)-dimensional modified dispersive water wave...
  • 65. Gao, X.Y., Guo, Y.J., Shan, W.R.: Symbolically computing the shallow water via a (2+1)-dimensional generalized modified dispersive...
  • 66. Bluman, G.W., Kumei, S.: Symmetries and Differential Equations. Springer, Berlin (1989)
  • 67. Rui, W., Zhang, Y., Yang, F.: Group classification and conservation laws of a sixth-order thin film type equation. Nonlinear Anal. 43,...
  • 68. Albares, P., Conde, J.M., Estévez, P.G.: Spectral problem for a two-component nonlinear Schrödinger equation in (2+1) dimensions:...
  • 69. Liu, F.Y., Gao, Y.T.: Lie group analysis for a higher-order Boussinesq-Burgers system. Appl. Math. Lett. 132, 108094 (2022)
  • 70. Olver, P.J.: Application of Lie Group to Differential Equations. Springer, New York (2000)
  • 71. Abdulwahhab, M.A.: Optimal system and exact solutions for the generalized system of 2-dimensional Burgers equations with infinite Reynolds...
  • 72. Ayhan, B., Bekir, A.: The G’/G-expansion method for the nonlinear lattice equations. Commun. Nonlinear Sci. Numer. Simul. 17, 3490–3498...
  • 73. Huang, W.H.: A polynomial expansion method and its application in the coupled Zakharov-Kuznetsov equations. Chaos Solitons Fract. 29,...
  • 74. Kong, L.Q., Dai, C.Q.: Some discussions about variable separation of nonlinear models using Riccati equation expansion method. Nonlinear...