Auto-Bäcklund Transformation and Exact Solutions for a New Integrable (3+1)-dimensional KdV-CBS Equation

• Xinyue Guo ^[1] ; Lianzhong Li ^[1]
  1. [1] Jiangnan University

     Jiangnan University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº 5, 2024
• Idioma: inglés
• DOI: 10.1007/s12346-024-01062-4
• Enlaces
  • Texto completo
• Resumen

  • The Korteweg-de Vries–Calogero–Bogoyavlenskii–Schiff (KdV-CBS) equation is often used in dealing with long-wave propagation interactions, and is widely used in mathematics, physics, and engineering. This paper proposes a new extended (3+1)- dimensional KdV-CBS equation, and it’s never been studied. Additionally, we verify the integrability of the equation based on the Painlevé test. By employing Hirota’s method, a bilinear auto-Bäcklund transformation, the multiple-soliton solutions, and the soliton molecules of the equation are derived. New exact solutions of the equation are constructed utilizing the power series expansion method and (G /G)-expansion method. These exact solutions are also presented graphically. Finally, the conservation laws of the equation are obtained. Our results are helpful for understanding nonlinear wave phenomena.

• Referencias bibliográficas
  • 1. Khater, M.M.A.: Novel computational simulation of the propagation of pulses in optical fibers regarding the dispersion effect. Int. J....
  • 2. Khater, M.M.A.: Abundant and accurate computational wave structures of the nonlinear fractional biological population model. Int. J. Mod....
  • 3. Khater, M.M.A.: Numerous accurate and stable solitary wave solutions to the generalized modified equal-width equation. Int. J. Theor. Phys....
  • 4. Khater, M.M.A.: Horizontal stratification of fluids and the behavior of long waves. Eur. Phys. J. Plus. 138(8), 715 (2023). https://doi.org/10.1140/epjp/s13360-023-04336-z
  • 5. Houwe, A., Abbagari, S., Akinyemi, L., et al.: Modulation instability, bifurcation analysis and solitonic waves in nonlinear optical media...
  • 6. Abdelwahab, A.M., Mekheimer, K.S., Ali, K.K., et al.: Numerical simulation of electroosmotic force on micropolar pulsatile bloodstream...
  • 7. Mekheimer, K.S., Abo-Elkhair, R.E., Ali, K.K., et al.: Entropy generation and curvature effect on peristaltic thrusting of (Cu-Al2O3) hybrid...
  • 8. Chen, J., Zhu, S.: Residual symmetries and soliton-cnoidal wave interaction solutions for the negativeorder Korteweg-de Vries equation....
  • 9. Wazwaz, A.M.: Multiple-soliton solutions for the Calogero-Bogoyavlenskii-Schiff, Jimbo-Miwa and YTSF equations. Appl. Math. Comput. 203(2),...
  • 10. Hasan, F.L., Abdoon, M.A.: The generalized (2+1) and (3+1)-dimensional with advanced analytical wave solutions via computational...
  • 11. Li, B., Chen, Y.: Exact analytical solutions of the generalized Calogero-Bogoyavlenskii-Schiff equation using symbolic computation. Czech....
  • 12. Wazwaz, A.M.: The (2+1) and (3+1)-dimensional CBS equations: multiple soliton solutions and multiple singular soliton solutions....
  • 13. Jadaun, V., Kumar, S.: Lie symmetry analysis and invariant solutions of (3+1)-dimensional CalogeroBogoyavlenskii-Schiff equation....
  • 14. Cinar,M., Secer, A., Bayram,M.: Analytical solutions of (2+1)-dimensional Calogero-BogoyavlenskiiSchiff equation in fluid mechanics/plasma...
  • 15. Wazwaz, A.M.: Two new Painlevé integrable KdV-Calogero-Bogoyavlenskii-Schiff (KdV-CBS) equation and new negative-order KdV-CBS equation....
  • 16. Gandarias, M.L., Raza, N.: Conservation laws and travelling wave solutions for a negative-order KdV-CBS equation in 3+1 dimensions....
  • 17. Raza, N., Arshed, S., Wazwaz, A.M.: Structures of interaction between lump, breather, rogue and periodic wave solutions for new (3+1)-dimensional...
  • 18. Singh, S., Ray, S.S.: Painlevé integrability and analytical solutions of variable coefficients negative order KdV-Calogero-Bogoyavlenskii-Schiff...
  • 19. Ma, Y., Wazwaz, A.M., Li, B.: A new (3+1)-dimensional Sakovich equation in nonlinear wave motion: Painlevé integrability, multiple...
  • 20. Li, B., Wazwaz, A.M., Ma, Y.: Two new types of nonlocal Boussinesq equations in water waves: bright and dark soliton solutions. Chinese...
  • 21. Ma, Y., Wazwaz, A.M., Li, B.: New extended Kadomtsev-Petviashvili equation: multiple soliton solutions, breather, lump and interaction...
  • 22. Ma, Y., Wazwaz, A.M., Li, B.: A new (3+1)-dimensional Kadomtsev-Petviashvili equation and its integrability, multiple-solitons, breathers...
  • 23. Akinyemi, L., Morazara, E.: Integrability, multi-solitons, breathers, lumps and wave interactions for generalized extended Kadomtsev-Petviashvili...
  • 24. Kaplan, M., Ozer, M.N.: Auto-Bäcklund transformations and solitary wave solutions for the nonlinear evolution equation. Opt. Quant. Electron....
  • 25. Kaplan, M., Ozer, M.N.: Multiple-soliton solutions and analytical solutions to a nonlinear evolution equation. Opt. Quant. Electron. 50,...
  • 26. Kaplan, M., Akbulut, A., Bekir, A.: The Auto-Bäcklund transformations for the (2+1)-dimensional Boiti-Leon-Manna-Pempinelli equation....
  • 27. Hirota, R.: The direct method in soliton theory. Cambridge University Press, Cambridge (2004)
  • 28. Alhami, R., Alquran, M.: Extracted different types of optical lumps and breathers to the new generalized stochastic potential-KdV equation...
  • 29. Alquran, M.: Classification of single-wave and bi-wave motion through fourth-order equations generated from the Ito model. Phys. Scr....
  • 30. Alquran, M., Alhami, R.: Analysis of lumps, single-stripe, breather-wave, and two-wave solutions to the generalized perturbed-KdV equation...
  • 31. Al-Deiakeh, R., Alquran, M., Ali, M., et al.: On group of Lie symmetry analysis, explicit series solutions and conservation laws for the...
  • 32. Liu, H., Geng, Y.: Symmetry reductions and exact solutions to the systems of carbon nanotubes conveying fluid. J. Differ. Equ. 254(5),...
  • 33. Mohammed, W.W., Alesemi, M., Albosaily, S., Iqbal, N., El-Morshedy, M.: The exact solutions of stochastic fractional-space Kuramoto-Sivashinsky...
  • 34. Zhang, S., Manafian, J., Ilhan, O.A., et al.: Nonparaxial pulse propagation to the cubic-quintic nonlinear Helmholtz equation. Int. J....
  • 35. Almusawa, H., Ali, K.K., Wazwaz, A.M., et al.: Protracted study on a real physical phenomenon generated by media inhomogeneities. Results...
  • 36. Khater, M.M.A.: Advancements in computational techniques for precise solitary wave solutions in the (1+1)-dimensional Mikhailov-Novikov-Wang...
  • 37. Han, T., Khater, M.M.A.: Numerical and computational investigation of soliton propagation in physical systems via computational schemes:...
  • 38. Khater, M.M.A.: Characterizing shallow water waves in channels with variable width and depth; computational and numerical simulations....
  • 39. Khater, M.M.A.: Computational simulations of propagation of a tsunami wave across the ocean. Chaos Solitons Fract. 174, 113806 (2023)....
  • 40. Yusuf, A., Sulaiman, T.A., Abdeljabbar, A., et al.: Breather waves, analytical solutions and conservation laws using Lie-Bäcklund symmetries...
  • 41. Alquran, M.: New interesting optical solutions to the quadratic-cubic Schrodinger equation by using the Kudryashov-expansion method and...
  • 42. Ali, M., Alquran, M., Salman, O.B.: A variety of new periodic solutions to the damped (2+1)- dimensional Schrodinger equation via...
  • 43. Khater, M.M.A.: Long waves with a small amplitude on the surface of the water behave dynamically in nonlinear lattices on a non-dimensional...
  • 44. Khater, M.M.A.: Soliton propagation under diffusive and nonlinear effects in physical systems; (1+1)- dimensional MNW integrable equation....
  • 45. Kumar, A., Kumar, S.: Dynamic nature of analytical soliton solutions of the (1+1)-dimensional Mikhailov-Novikov-Wang equation using...
  • 46. Hussain, A., Ali, H., Zaman, F., et al.: New closed form solutions of some nonlinear pseudo-parabolic models via a new extended direct...
  • 47. Sivasundaram, S., Kumar, A., Singh, R.K.: On the complex properties to the first equation of the Kadomtsev-Petviashvili hierarchy. Int....
  • 48. Bilal, M., Haris, H., Waheed, A., et al.: The analysis of exact solitons solutions in monomode optical fibers to the generalized nonlinear...
  • 49. Osman, M.S., Ali, K.K.: Optical soliton solutions of perturbing time-fractional nonlinear Schrödinger equations. Optik. 209, 164589 (2020)....
  • 50. Al-Amr, M.O., Rezazadeh, H., Ali, K.K., et al.: N1-soliton solution for Schrödinger equation with competing weakly nonlocal and parabolic...
  • 51. Wazwaz, A.M., El-Sherif, L., El-Tantawy, S.: Integrability features of a new (3+1)-dimensional nonlinear Hirota bilinear model: multiple...
  • 52. Ma, Y., Wazwaz, A.M., Li, B.: Phase transition from soliton to breather, soliton-breather molecules, breather molecules of the Caudrey-Dodd-Gibbon...
  • 53. Ma, Y., Wazwaz, A.M., Li, B.: Soliton resonances, soliton molecules, soliton oscillations and heterotypic solitons for the nonlinear Maccari...
  • 54. Li, B., Ma, Y.: Breather, soliton molecules, soliton fusions and fissions, and lump wave of the CaudreyDodd-Gibbon equation. Phys. Scr....
  • 55. Ma, Y., Li, B.: Interaction behaviors between solitons, breathers and their hybrid forms for a short pulse equation. Qual. Theory Dyn....
  • 56. Li, B., Ma, Y.: Hybrid soliton and breather waves, solution molecules and breather molecules of a (3+1)-dimensional Geng equation...
  • 57. Ma, Y., Li, B.: Bifurcation solitons and breathers for the nonlocal Boussinesq equations. Appl. Math. Lett. 124, 107677 (2022). https://doi.org/10.1016/j.aml.2021.107677
  • 58. Qian, Y., Manafian, J., Asiri, M., et al.: Nonparaxial solitons and the dynamics of solitary waves for the coupled nonlinear Helmholtz...
  • 59. Li, R., Manafian, J., Lafta, H.A., et al.: The nonlinear vibration and dispersive wave systems with cross-kink and solitary wave solutions....
  • 60. Li, R., Sinnah, Z.A.B., Shatouri, Z.M., et al.: Different forms of optical soliton solutions to the Kudryashov’s quintuple self-phase...
  • 61. Liu, X., Abd, Alreda, B., Manafian, J., et al.: Computational modeling of wave propagation in plasma physics over the Gilson-Pickering...
  • 62. Akinyemi, L., Houwe, A., Abbagari, S., et al.: Effects of the higher-order dispersion on solitary waves and modulation instability in...
  • 63. Mirzazadeh, M., Akbulut, A., Ta¸scan, F., et al.: A novel integration approach to study the perturbed Biswas-Milovic equation with Kudryashov’s...
  • 64. Ibragimov, N.H.: A new conservation theorem. J. Math. Anal. Appl. 333(1), 311–328 (2007). https:// doi.org/10.1016/j.jmaa.2006.10.078