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Hetero-Bäcklund Transformation, Bilinear Forms and N Solitons for a Generalized Three-Coupled Korteweg-de Vries System

  • Gao, Xin-Yi [1] ; Guo, Yong-Jiang [1] ; Shan, Wen-Rui [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. 20, Nº 3, 2021
  • Idioma: inglés
  • DOI: 10.1007/s12346-021-00512-7
  • Enlaces
  • Resumen

    • Korteweg-de Vries-type models attract people’s attention during the studies on the cosmic plasmas, planetary oceans and atmospheres. In this paper, on a generalized three-coupled Korteweg-de Vries system, symbolic computation comes to a hetero-Bäcklund transformation, while the Hirota method and symbolic computation bring about some bilinear forms and multi-solutions. Our results are dependent on the coefficients in that system.

  • Referencias bibliográficas
    • 1. Chentouf, B.: Qualitative analysis of the dynamic for the nonlinear Korteweg-de Vries equation with a boundary memory. Qual. Theory Dyn....
    • 2. Dhama, S., Abbas, S.: Existence and stability of weighted pseudo almost automorphic solution of dynamic equation on time scales with weighted...
    • 3. Aziz, W.: Integrability and Linearizability Problems of Three Dimensional Lotka-Volterra equations of rank-2. Qual. Theory Dyn. Syst. 18,...
    • 4. Bihun, O., Calogero, F.: Time-dependent polynomials with one double root, and related new solvable systems of nonlinear evolution equations....
    • 5. Li, L.Q., Gao, Y.T., Hu, L., Jia, T.T., Ding, C.C., Feng, Y.J.: Bilinear form, soliton, breather, lump and hybrid solutions for a (2+1)-dimensional...
    • 6. Velasco-Juan, M., Fujioka, J.: Integral complex modified Korteweg-de Vries (Icm-KdV) equations. Chaos Solitons Fract. 134, 109687 (2020)
    • 7. Akinyemi, L., Iyiola, O.S.: A reliable technique to study nonlinear time-fractional coupled Korteweg-de Vries equations. Adv. Differ. Equ....
    • 8. Akinyemi, L.: q-Homotopy analysis method for solving the seventh-order time-fractional Lax’s Korteweg-de Vries and Sawada-Kotera equations....
    • 9. Karunakar, P., Chakraverty, S.: Solutions of time-fractional third- and fifth-order Korteweg-de-Vries equations using homotopy perturbation...
    • 10. Ahmed, H.M.: Numerical Solutions of Korteweg-de Vries and Korteweg-de Vries-Burger’s Equations in a Bernstein Polynomial Basis. Mediterr....
    • 11. Popowicz, Z.: N=2 Supercomplexification of the Korteweg-de Vries, Sawada-Kotera and KaupKupershmidt Equations. J. Nonlinear Math....
    • 12. Franco-de-Leon, M., Lowengrub, J.: Boundary integral methods for dispersive equations, Airy flow and the modified Korteweg de Vries equation....
    • 13. Tobisch, E., Pelinovsky, E.: Conditions for modulation instability in higher order Korteweg-de Vries equations. Appl. Math. Lett. 88,...
    • 14. Harms, P., Muller, M.S.: Weak convergence rates for stochastic evolution equations and applications to nonlinear stochastic wave, HJMM,...
    • 15. Gao, X.Y., Guo, Y.J., Shan, W.R.: Cosmic dusty plasmas via a (3+1)-dimensional generalized variablecoefficient Kadomtsev-Petviashvili-Burgers-type...
    • 16. 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...
    • 17. Wang, D., Gao, Y.T., Ding, C.C., Zhang, C.Y.: Solitons and periodic waves for a generalized (3+1)- dimensional Kadomtsev-Petviashvili...
    • 18. Shen, Y., Tian, B., Liu, S.H., Yang, D.Y.: Bilinear Bäcklund transformation, soliton and breather solutions for a (3+1)-dimensional...
    • 19. Ding, C.C., Gao, Y.T., Deng, G.F.: Breather and hybrid solutions for a generalized (3+1)-dimensional B-type Kadomtsev-Petviashvili...
    • 20. Liu, S.H., Tian, B., Qu, Q.X., Li, H., Zhao, X.H., Du, X.X., Chen, S.S.: Breather, lump, shock and travelling-wave solutions for a (3+1)-dimensional...
    • 21. Chen, Y.Q., Tian, B., Qu, Q.X., Li, H., Zhao, X.H., Tian, H.Y., Wang, M.: Ablowitz-Kaup-NewellSegur system, conservation laws and Backlund...
    • 22. Shen, Y., Tian, B.: Bilinear auto-Bäcklund transformations and soliton solutions of a (3+1)-dimensional generalized nonlinear evolution...
    • 23. Chen, Y.Q., Tian, B., Qu, Q.X., Li, H., Zhao, X.H., Tian, H.Y., Wang, M.: Reduction and analytic solutions of a variable-coefficient Korteweg-de...
    • 24. Hu, C.C., Tian, B., Yin, H.M., Zhang, C.R., Zhang, Z.: Dark breather waves, dark lump waves and lump wave-soliton interactions for a (3+1)-dimensional...
    • 25. 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...
    • 26. Shen, Y., Tian, B., Liu, S.H.: Solitonic fusion and fission for a (3+1)-dimensional generalized nonlinear evolution equation arising...
    • 27. Deng, G.F., Gao, Y.T., Ding, C.C., Su, J.J.: Solitons and breather waves for the generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt...
    • 28. Wang, M., Tian, B., Liu, S.H., Shan, W.R., Jiang, Y.: Soliton, multiple-lump and hybrid solutions of a (2+1)-dimensional generalized...
    • 29. Liu, S.H., Tian, B., Qu, Q.X., Zhang, C.R., Hu, C.C., Wang, M.: Lump, mixed lump-stripe, mixed rogue wave-stripe and breather wave solutions...
    • 30. 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,...
    • 31. Shen, Y., Tian, B., Zhou, T.Y.: In nonlinear optics, fluid dynamics and plasma physics: symbolic computation on a (2+1)-dimensional...
    • 32. Hu, L., Gao, Y.T., Jia, S.L., Su, J.J., Deng, G.F.: Solitons for the (2+1)-dimensional Boiti-Leon-MannaPempinelli equation for an...
    • 33. Wang, M., Tian, B., Sun, Y., Zhang, Z.: Lump, mixed lump-stripe and rogue wave-stripe solutions of a (3+1)-dimensional nonlinear wave...
    • 34. Liu, F.Y., Gao, Y.T., Yu, X., Li, L.Q., Ding, C.C., Wang, D.: Lie group analysis and analytic solutions for a (2+1)-dimensional generalized...
    • 35. Shen, Y., Tian, B., Zhang, C.R., Tian, H.Y., Liu, S.H.: Breather-wave, periodic-wave and traveling-wave solutions for a (2+1)-dimensional...
    • 36. 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...
    • 37. Ma, Y.X., Tian, B., Qu, Q.X., Wei, C.C., Zhao, X.: Bäcklund transformations, kink soliton, breatherand travelling-wave solutions for a...
    • 38. Gao, X.Y., Guo, Y.J., Shan, W.R.: Auto- and hetero-Bäcklund transformations for a generalized threecoupled Korteweg-de Vries system. Rom....
    • 39. Korteweg, D.J., de Vries, G.: On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary...
    • 40. Du, X.X., Tian, B., Yuan, Y.Q., Zhang, C.R., Du, Z.: Symmetry reductions, group-invariant solutions and conservation laws of a three-coupled...
    • 41. Zhao, Y., Gu, Z.Q., Liu, Y.F.: The Neumann system for the 4th-order eigenvalue problem and constraint flows of the coupled KdV-type equations....
    • 42. Zuo, D.W., Gao, Y.T., Meng, G.Q., Shen, Y.J., Yu, X.: Multi-soliton solutions for the three-coupled KdV equations engendered by the Neumann...
    • 43. Biswas, A., Ismail, M.S.: 1–Soliton solution of the coupled KdV equation and Gear–Grimshaw model. Appl. Math.Comput. 216, 3662–3670 (2010)
    • 44. Hu, X., Li, Y.: Nonlocal symmetry and soliton–cnoidal wave solutions of the Bogoyavlenskii coupled KdV system. Appl. Math. Lett. 51, 20–26...
    • 45. Hu, H.C., Lou, S.Y.: Exact Solutions of Bogoyavlenskii Coupled KdV Equations. Commun. Theor. Phys. 42, 485–487 (2004)
    • 46. Tian, B., Gao, Y.T.: Exact solutions for the Bogoyavlenskii coupled KdV equations. Phys. Lett. A 208, 193–196 (1995)
    • 47. Verhoeven C., Musette, M.: Grammian N–soliton solutions of a coupled KdV system. J. Phys. A 34, L721–L725 (2001)
    • 48. 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...
    • 49. Gao, X.Y., Guo, Y.J., Shan, W.R.: Shallow water in an open sea or a wide channel: Auto-and nonauto-Bäcklund transformations with solitons...
    • 50. Gao, X.Y., Guo, Y.J., Shan, W.R.: Beholding the shallow water waves near an ocean beach or in a lake via a Boussinesq-Burgers system....
    • 51. Gao, X.Y., Guo, Y.J., Shan, W.R.: Hetero-Bäcklund transformation and similarity reduction of an extended (2+1)-dimensional coupled...
    • 52. Gao, X.Y., Guo, Y.J., Shan, W.R.: Scaling and hetero–/auto–Backlund transformations with solitons of an extended coupled (2+1)–dimensional...
    • 53. Shen, Y., Tian, B., Zhao, X., Shan, W.R., Jiang, Y.: Bilinear form, bilinear auto-Bäcklund transformation, breather and lump solutions...
    • 54. 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+1)-dimensional...
    • 55. 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...
    • 56. Zhao, X., Tian, B., Tian, H.Y., Yang, D.Y.: Bilinear Bäcklund transformation, Lax pair and interactions of nonlinear waves for a generalized...
    • 57. Gao, X.Y., Guo, Y.J., Shan, W.R.: Water-wave symbolic computation for the Earth, Enceladus and Titan: The higher-order Boussinesq-Burgers...
    • 58. 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...
    • 59. Zhang, C.R., Tian, B., Sun, Y., Yin, H.M.: Binary Darboux transformation and vector-soliton-pair interactions with the negatively coherent...
    • 60. Du, X.X., Tian, B., Yuan, Y.Q., Du, Z.: Symmetry reductions, group-invariant solutions, and conservation laws of a (2+1)-dimensional...
    • 61. Su, J.J., Gao, Y.T., Deng, G.F., Jia, T.T.: Solitary waves, breathers, and rogue waves modulated by long waves for a model of a baroclinic...
    • 62. Tian, H.Y., Tian, B., Yuan, Y.Q., Zhang, C.R.: Superregular solutions for a coupled nonlinear Schrödinger system in a two-mode nonlinear...
    • 63. 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...
    • 64. Chen, S.S., Tian, B., Chai, J., Wu, X.Y., Du, Z.: Lax pair, binary Darboux transformations and darksoliton interaction of a fifth-order...
    • 65. Ding, C.C., Gao, Y.T., Deng, G.F., Wang, D.: Lax pair, conservation laws, Darboux transformation, breathers and rogue waves for the coupled...
    • 66. Wang, M., Tian, B., Hu, C.C., Liu, S.H.: Generalized Darboux transformation, solitonic interactions and bound states for a coupled fourth-order...
    • 67. Yang, D.Y., Tian, B., Qu, Q.X., Li, H., Zhao, X.H., Chen, S.S., Wei, C.C.: Darboux-dressing transformation, semi-rational solutions, breathers...
    • 68. Zhao, X., Tian, B., Qu, Q.X., Yuan, Y.Q., Du, X.X., Chu, M.X.: Dark-dark solitons for the coupled spatially modulated Gross-Pitaevskii...
    • 69. Hirota, R.: The Direct Method in Soliton Theory. Springer, Berlin (1980)
    • 70. Wang, D., Gao, Y.T., Su, J.J., Ding, C.C.: Bilinear forms and soliton solutions for a (2+1)-dimensional variable-coefficient nonlinear...
    • 71. Jia, T.T., Gao, Y.T., Deng, G.F., Hu, L.: Quintic time-dependent-coefficient derivative nonlinear Schrödinger equation in hydrodynamics...
    • 72. Feng, Y.J., Gao, Y.T., Li, L.Q., Jia, T.T.: Bilinear form, solitons, breathers and lumps of a (3+1)- dimensional generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt...
    • 73. Wang, D., Gao, Y.T., Yu, X., Li, L.Q., Jia, T.T.: Bilinear form, solitons, breathers, lumps and hybrid solutions for a (3+1)-dimensional...
    • 74. Jia, T.T., Gao, Y.T., Yu, X., Li, L.Q.: Lax pairs, Darboux transformation, bilinear forms and solitonic interactions for a combined Calogero-Bogoyavlenskii-Schiff-type...
    • 75. 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...
    • 76. 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...
    • 77. Feng, Y.J., Gao, Y.T., Jia, T.T., Li, L.Q.: Soliton interactions of a variable-coefficient three-component AB system for the geophysical...
    • 78. Du, X.X., Tian, B., Qu, Q.X., Yuan, Y.Q., Zhao, X.H.: Lie group analysis, solitons, self-adjointness and conservation laws of the modified...
    • 79. Zhang, C.R., Tian, B., Qu, Q.X., Liu, L., Tian, H.Y.: Vector bright solitons and their interactions of the couple Fokas-Lenells system...
    • 80. 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...
    • 81. Su, J.J., Gao, Y.T., Ding, C.C.: Darboux transformations and rogue wave solutions of a generalized AB system for the geophysical flows....
    • 82. Tian, H.Y., Tian, B., Zhang, C.R., Chen, S.S.: Darboux dressing transformation and superregular breathers for a coupled nonlinear Schrödinger...
    • 83. Deng, G.F., Gao, Y.T., Su, J.J., Ding, C.C., Jia, T.T.: Solitons and periodic waves for the (2+1)- dimensional generalized Caudrey-Dodd-Gibbon-Kotera-Sawada...
    • 84. Chen, S.S., Tian, B., Sun, Y., Zhang, C.R.: Generalized Darboux Transformations, Rogue Waves, and Modulation Instability for the Coherently...
    • 85. 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...
    • 86. Wei, C.C., Tian, B., Qu, Q.X., Chen, S.S., Yang, D.Y.: Lax pair, Darboux transformation and rogueperiodic waves of a nonlinear Schrodinger-Hirota...
    • 87. Yang, D.Y., Tian, B., Tian, H.Y., Chen, Y.Q., Shan, W.R., Jiang, Y.: Interaction between the breather and breather-like soliton, and breather-to-soliton...
    • 88. Satsuma, J., Hirota, R.: A coupled KdV equation is one case of the four-reduction of the KP hierarchy. J. Phys. Soc. Jpn. 51, 3390–3397...
    • 89. Matsuno, Y.: Bilinear Transformation Method. Acad., Orlando (1984)
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