Auto-Bäcklund Transformation, Similarity Reductions and Solitons of an Extended (2 + 1)-Dimensional Coupled Burgers System in Fluid Mechanics

• Xin-Yi Gao ^[1] ; Yong-Jiang Guo ^[1] ; Wen-Rui Shan ^[1]
  1. [1] Beijing University of Posts and Telecommunications

     Beijing University of Posts and Telecommunications

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 21, Nº 3, 2022
• Idioma: inglés
• Enlaces
  • Texto completo (pdf)
• Resumen

  • Burgers-type equations are seen in cosmology, hydrodynamics, plasma physics, hurricane dynamics, statistical dynamics, traffic modelling, etc. For an extended (2+1)-dimensional coupled Burgers system in fluid mechanics, concerning the velocity components in the fluid-related problems, our symbolic computation brings forth an auto-Bäcklund transformation with some solitons, and two sets of the similarity reductions. Our results rely on the coefficients in the system.

• Referencias bibliográficas
  • 1. Leta, T.D., Liu, W., Rezazadeh, H., Ding, J., El Achab, A.: Analytical traveling wave and soliton solutions of the (2 + 1) dimensional...
  • 2. Chentouf, B.: Qualitative analysis of the dynamic for the nonlinear Korteweg-de Vries equation with a boundary memory. Qual. Theory Dyn....
  • 3. Gao, X.Y., Guo, Y.J., Shan, W.R.: Hetero-Bäcklund transformation, bilinear forms and N solitons for a generalized three-coupled Korteweg-de...
  • 4. Gao, X.Y., Guo, Y.J., Shan, W.R.: Scaling and hetero-/auto-Bäcklund transformations with solitons of an extended coupled (2 + 1)-dimensional...
  • 5. Gao, X.Y., Guo, Y.J., Shan, W.R.: In oceanography, acoustics and hydrodynamics: an extended coupled (2 + 1)-dimensional Burgers system....
  • 6. Gao, X.Y., Guo, Y.J., Shan, W.R.: Hetero-Bäcklund transformation and similarity reduction of an extended (2 + 1)-dimensional coupled...
  • 7. Osman, M.S., Baleanu, D., Adem, A.R., Hosseini, K., Mirzazadeh, M., Eslami, M.: Double-wave solutions and Lie symmetry analysis to the...
  • 8. Wang, G.W., Liu, Y.X., Han, S.X., Wang, H., Su, X.: Generalized symmetries and mCK method analysis of the (2 + 1)-dimensional coupled...
  • 9. Wazwaz, A.M.: Multiple-front solutions for the Burgers equation and the coupled Burgers equations. Appl. Math. Comput. 190, 1198 (2007)
  • 10. Wang, G.W., Xu, T.Z., Biswas, A.: Topological solitons and conservation laws of the coupled Burgers equations. Rom. Rep. Phys. 66, 274...
  • 11. Srivastava, V.K., Singh, S., Awasthi, M.K.: Numerical solutions of coupled Burgers’ equations by an implicit finite-difference scheme....
  • 12. Siraj-ul-Islam, Sarler, B., Vertnik, R., Kosec, G.: Radial basis function collocation method for the numerical solution of the two-dimensional...
  • 13. Ali, A., Siraj-ul-Islam, Haq, S.: A computational meshfree technique for the numerical solution of the two-dimensional coupled Burgers’...
  • 14. Wang, G.W., Fakhar, K., Kara, A.H.: Soliton solutions and group analysis of a new coupled (2 + 1)- dimensional Burgers equations....
  • 15. Liu, F.Y., Gao, Y.T.: Lie group analysis for a higher-order Boussinesq-Burgers system. Appl. Math. Lett. (2022). https://doi.org/10.1016/j.aml.2022.108094
  • 16. Gao, X.T., Tian, B., Feng, C.H.: Comment on “In oceanography, acoustics and hydrodynamics: An extended coupled (2 + 1)-dimensional...
  • 17. Wang, M., Tian, B., Zhou, T.Y.: Darboux transformation, generalized Darboux transformation and vector breathers for a matrix Lakshmanan-Porsezian-Daniel...
  • 18. Yang, D.Y., Tian, B., Hu, C.C., Liu, S.H., Shan, W.R., Jiang, Y.: Conservation laws and breather-tosoliton transition for a variable-coefficient...
  • 19. Wu, X.H., Gao, Y.T., Yu, X., Ding, C.C., Liu, F.Y., Jia, T.T.: Darboux transformation, bright and darkbright solitons of an N-coupled...
  • 20. Tian, H.Y., Tian, B., Zhang, C.R., Chen, S.S.: Darboux dressing transformation and superregular breathers for a coupled nonlinear Schrödinger...
  • 21. Wang, M., Tian, B.: Darboux transformation, generalized Darboux transformation and vector breather solutions for the coupled variable-coefficient...
  • 22. Yang, D.Y., Tian, B., Qu, Q.X., Du, X.X., Hu, C.C., Jiang, Y., Shan, W.R.: Lax pair, solitons, breathers and modulation instability of...
  • 23. Lu, Y.L., Wei, G.M., Liu, X.: Lax Pair, improved -Riccati Backlund transformation and soliton-like solutions to variable-coefficient higher-order...
  • 24. Wang, M., Tian, B.: In an inhomogeneous multicomponent optical fiber: Lax pair, generalized Darboux transformation and vector breathers...
  • 25. Yang, D.Y., Tian, B., Tian, H.Y., Wei, C.C., Shan, W.R., Jiang, Y.: Darboux transformation, localized waves and conservation laws for...
  • 26. Yu, X., Sun, Z.Y.: Parabola solitons for the nonautonomous KP equation in fluids and plasmas. Ann. Phys. 367, 251 (2016)
  • 27. Wang, M., Tian, B.: Lax pair, generalized Darboux transformation and solitonic solutions for a variablecoefficient coupled Hirota system...
  • 28. Yang, D.Y., Tian, B., Wang, M., Zhao, X., Shan, W.R., Jiang, Y.: Lax pair, Darboux transformation, breathers and rogue waves of an N-coupled...
  • 29. Ma, Y.L., Wazwaz, A.M., Li, B.Q.: New extended Kadomtsev-Petviashvili equation: multiple soliton solutions, breather, lump and interaction...
  • 30. Young, D.L., Fan, C.M., Hu, S.P., Atluri, S.N.: The Eulerian-Lagrangian method of fundamental solutions for two-dimensional unsteady Burgers’...
  • 31. Shankar, R., Singh, T.V., Bassaif, A.A.: Numerical solution of coupled burgers equations in inhomogeneous form. Int. J. Numer. Methods...
  • 32. Bahadir, A.R.: A fully implicit finite-difference scheme for two-dimensional Burgers’ equations. Appl. Math. Comput. 137, 131 (2003)
  • 33. Zafarghandi, F.S., Mohammadi, M., Babolian, E., Javadi, S.: A localized Newton basis functions meshless method for the numerical solution...
  • 34. Wubs, F.W., de Goede, E.D.: An explicit-implicit method for a class of time-dependent partial differential equations. Appl. Numer. Math....
  • 35. Fletcher, C.A.: Generating exact solutions of the two-dimensional Burgers’ equation. Int. J. Numer. Methods Fluids 3, 213 (1983)
  • 36. Abazari, R., Borhanifar, A.: Numerical study of the solution of the Burgers and coupled Burgers equations by a differential transformation...
  • 37. Abdou, M.A., Soliman, A.A.: On completely integrable coupled Burgers and coupled Korteweg-de Vries systems. Appl. Math. Lett. 25, 2052...
  • 38. El-Sayed, S.M., Kaya, D.: On the numerical solution of the system of two-dimensional Burgers’ equations by the decomposition method. Appl....
  • 39. Lv, Z.S., Zhang, H.Q.: New applications of a further extended tanh method. Phys. Lett. A 324, 293 (2004)
  • 40. Ma, Z.Y., Wu, X.F., Zhu, J.M.: Multisoliton excitations for the Kadomtsev-Petviashvili equation and the coupled Burgers equation. Chaos...
  • 41. Ma, Z.Y., Fei, J.X., Chen, Y.M.: The residual symmetry of the (2 + 1)-dimensional coupled Burgers equation. Appl. Math. Lett. 37,...
  • 42. Wang, Q., Song, L.N., Zhang, H.Q.: A new coupled sub-equations expansion method and novel complexiton solutions of (2 + 1)-dimensional...
  • 43. Lei, Y., Yang, D.: Finite symmetry transformation group and localized structures of (2+1)-dimensional coupled Burgers equation. Chin....
  • 44. Wazwaz, A.M.: Multiple kink solutions and multiple singular kink solutions for the (2+1)-dimensional Burgers equations. Appl. Math....
  • 45. El-Sayed, M.F., Moatimid, G.M., Moussa, M.H., El-Shiekh, R.M., El-Satar, A.A.: Symmetry group analysis and similarity solutions for the...
  • 46. Ding, C.C., Gao, Y.T., Hu, L., Deng, G.F., Zhang, C.Y.: Vector bright soliton interactions of the twocomponent AB system in a baroclinic...
  • 47. Liu, F.Y., Gao, Y.T., Yu, X., Hu, L., Wu, X.H.: Hybrid solutions for the (2 + 1)-dimensional variablecoefficient Caudrey-Dodd-Gibbon-Kotera-Sawada...
  • 48. Hu, L., Gao, Y.T., Jia, S.L., Su, J.J., Deng, G.F.: Solitons for the (2 + 1)-dimensional Boiti-LeonManna-Pempinelli equation for an...
  • 49. Wang, M., Tian, B., Qu, Q.X., Zhao, X.H., Zhang, Z., Tian, H.Y.: Lump, lumpoff, rogue wave, breather wave and periodic lump solutions...
  • 50. Shen, Y., Tian, B., Zhou, T.Y.: In nonlinear optics, fluid dynamics and plasma physics: symbolic computation on a (2 + 1)-dimensional...
  • 51. Gao, X.Y., Guo, Y.J., Shan, W.R.: Looking at an open sea via a generalized (2+1)-dimensional dispersive long-wave system for the shallow...
  • 52. Hu, L., Gao, Y.T., Jia, T.T., Deng, G.F., Li, L.Q.: Higher-order hybrid waves for the (2+1)-dimensional Boiti-Leon-Manna-Pempinelli...
  • 53. Wang, M., Tian, B., Sun, Y., Yin, H.M., Zhang, Z.: Mixed lump-stripe, bright rogue wave-stripe, dark rogue wave-stripe and dark rogue...
  • 54. Shen, Y., Tian, B., Zhou, T.Y., Gao, X.T.: Shallow-water-wave studies on a (2+1)-dimensional HirotaSatsuma-Ito system: X-type soliton,...
  • 55. Wang, M., Tian, B., Qu, Q.X., Du, X.X., Zhang, C.R., Zhang, Z.: Lump, lumpoff and rogue waves for a (2+1)-dimensional reduced Yu-Toda-Sasa-Fukuyama...
  • 56. Liu, F.Y., Gao, Y.T., Yu, X., Ding, C.C.: Wronskian, Gramian, Pfaffian and periodic-wave solutions for a (3+1)-dimensional generalized...
  • 57. Wang, M., Tian, B.: Soliton, multiple-lump, and hybrid solutions for a (3+1)-dimensional generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt...
  • 58. Gao, X.Y., Guo, Y.J., Shan, W.R.: Oceanic long-gravity-water-wave investigations on a variablecoefficient nonlinear dispersive-wave system....
  • 59. Hu, C.C., Tian, B., Zhao, X.: Rogue and lump waves for the (3 + 1)-dimensional Yu-Toda-SasaFukuyama equation in a liquid or lattice....
  • 60. Cheng, C.D., Tian, B., Zhang, C.R., Zhao, X.: Bilinear form, soliton, breather, hybrid and periodicwave solutions for a (3+1)-dimensional...
  • 61. Wang, M., Tian, B., Hu, C.C., Liu, S.H.: Generalized Darboux transformation, solitonic interactions and bound states for a coupled fourth-order...
  • 62. Liang, Y.Q., Wei, G.M., Li, X.N.: New variable separation solutions and nonlinear phenomena for the (2+1)-dimensional modified Korteweg...
  • 63. Yang, D.Y., Tian, B., Qu, Q.X., Zhang, C.R., Chen, S.S., Wei, C.C.: Lax pair, conservation laws, Darboux transformation and localized...
  • 64. Ding, C.C., Gao, Y.T., Yu, X., Liu, F.Y., Wu, X.H.: Three-wave resonant interactions: dark -bright -bright mixed N- and high-order solitons,...
  • 65. Chen, S.S., Tian, B., Qu, Q.X., Li, H., Sun, Y., Du, X.X.: Alfvén solitons and generalized Darboux transformation for a variable-coefficient...
  • 66. Shen, Y., Tian, B., Liu, S.H., Zhou, T.Y.: Studies on certain bilinear form, N-soliton, higher-order breather, periodic-wave and hybrid...
  • 67. Yu, X., Sun, Z.Y.: Unconventional characteristic line for the nonautonomous KP equation. Appl. Math. Lett. 100, 106047 (2020)
  • 68. Sun, Z.Y., Yu, X.: Transport of Nonautonomous Solitons in Two-Dimensional Disordered Media, Ann. Phys. (Berlin) 529, 1600323 (2017)
  • 69. Li, L.Q., Gao, Y.T., Yu, X., Deng, G.F., Ding, C.C.: Gramian solutions and solitonic interactions of a (2 + 1)-dimensional Broer-Kaup-Kupershmidt...
  • 70. Tian, H.Y., Tian, B., Sun, Y., Zhang, C.R.: Three-component coupled nonlinear Schrödinger system in a multimode optical fiber: Darboux...
  • 71. Gao, X.Y., Guo, Y.J., Shan, W.R.: Optical waves/modes in a multicomponent inhomogeneous optical fiber via a three-coupled variable-coefficient...
  • 72. Zhou, T.Y., Tian, B., Chen, Y.Q., Shen, Y.: Painlevé analysis, auto-Bäcklund transformation and analytic solutions of a (2+1)-dimensional...
  • 73. Gao, X.Y., Guo, Y.J., Shan, W.R., Yin, H.M., Du, X.X., Yang, D.Y.: Electromagnetic waves in a ferromagnetic film. Commun. Nonlinear Sci....
  • 74. Zhou, T.Y., Tian, B., Chen, S.S., Wei, C.C., Chen, Y.Q.: Bäcklund transformations, Lax pair and solutions of the Sharma-Tasso-Olver-Burgers...
  • 75. Liu, F.Y., Gao, Y.T., Yu, X., Ding, C.C., Deng, G.F., Jia, T.T.: Painlevé analysis, Lie group analysis and soliton-cnoidal, resonant,...
  • 76. Gao, X.Y., Guo, Y.J., Shan, W.R.: Bilinear forms through the binary Bell polynomials, N solitons and Bäcklund transformations of the Boussinesq-Burgers...
  • 77. Ma, Y.X., Tian, B., Qu, Q.X., Wei, C.C., Zhao, X.: Bäcklund transformations, kink soliton, breatherand travelling-wave solutions for a...
  • 78. Shen, Y., Tian, B., Gao, X.T.: Bilinear auto-Bäcklund transformation, soliton and periodic-wave solutions for a (2 + 1)-dimensional...
  • 79. Li, L.Q., Gao, Y.T., Yu, X., Jia, T.T., Hu, L., Zhang, C.Y.: Bilinear forms, bilinear Bäcklund transformation, soliton and breather interactions...
  • 80. Shen, Y., Tian, B., Cheng, C.D., Zhou, T.Y.: Bilinear auto-Bäcklund transformation, breather-wave and periodic-wave solutions for a (3+1)-dimensional...
  • 81. Ma, Y.X., Tian, B., Qu, Q.X., Tian, H.Y., Liu, S.H.: Bilinear Bäcklund transformation, breather- and travelling-wave solutions for a (2+1)-dimensional...
  • 82. Shen, Y., Tian, B., Zhao, X., Shan, W.R., Jiang, Y.: Bilinear form, bilinear auto-Bäcklund transformation, breather and lump solutions...
  • 83. Ma, Y.X., Tian, B., Qu, Q.X., Yang, D.Y., Chen, Y.Q.: Painlevé analysis, Bäcklund transformations and traveling-wave solutions for a (3...
  • 84. Shen, Y., Tian, B.: Bilinear auto-Bäcklund transformations and soliton solutions of a (3+1)-dimensional generalized nonlinear evolution...
  • 85. Gao, X.T., Tian, B., Shen, Y., Feng, C.H.: Comment on “Shallow water in an open sea or a wide channel: Auto- and non-auto-Bäcklund transformations...
  • 86. Gao, X.Y., Guo, Y.J., Shan, W.R.: Symbolic computation on a (2+1)-dimensional generalized variablecoefficient Boiti-Leon-Pempinelli...
  • 87. Gao, X.Y., Guo, Y.J., Shan, W.R.: Similarity reductions for a (3 + 1)-dimensional generalized Kadomtsev-Petviashvili equation in nonlinear...
  • 88. Gao, X.T., Tian, B.: Water-wave studies on a (2 + 1)-dimensional generalized variable-coefficient Boiti-Leon-Pempinelli system. Appl....
  • 89. Gao, X.Y., Guo, Y.J., Shan, W.R.: Scaling transformation, hetero-Bäcklund transformation and similarity reduction on a (2 + 1)-dimensional...
  • 90. Clarkson, P., Kruskal, M.: New similarity reductions of the Boussinesq equation. J. Math. Phys. 30, 2201 (1989)
  • 91. Zwillinger, D.: Handbook of Differential Equations, 3rd edn. Acad, San Diego (1997)
  • 92. Wei, G.M., Lu, Y.L., Xie, Y.Q., Zheng, W.X.: Lie symmetry analysis and conservation law of variablecoefficient Davey-Stewartson equation....
  • 93. Guan, S.N., Wei, G.M., Li, Q.: Lie symmetry analysis, optimal system and conservation law of a generalized (2+1)-dimensional Hirota-Satsuma-Ito...