Bilinear Forms, Bilinear Auto-Bäcklund Transformations and Similarity Reductions for a (3+1)-Dimensional Generalized Variable-Coefficient Korteweg-de VriesCalogero-Bogoyavlenskii-Schiff Equation in Quantum and Fluid Mechanics

• Xin-Yi Gao ^[1] ; Wei-Gang Zhao ^[2] ; Da-Wei Zuo ^[2]
  1. [1] North China University of Technology

     North China University of Technology

     China

     
  2. [2] Shijiazhuang Tiedao University

     Shijiazhuang Tiedao University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 5, 2025
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • In quantum and fluid mechanics, nonlinear models are reported, including a (3+1)- dimensional generalized variable-coefficient Korteweg-de Vries-Calogero-Bogoy avlenskii-Schiff equation describing the interaction between a long wave and a Riemann wave, which is the subject of this paper. For that equation, we find (A) a bilinear form, (B) a set of the bilinear auto-Bäcklund transformations with some soliton solutions and (C) a set of the similarity reductions. Our results, i.e., bilinear form, bilinear auto-Bäcklund transformations with solitons as well as similarity reductions, may help people investigate certain wave modes and dynamic features in quantum and fluid mechanics in the future.

• Referencias bibliográficas
  • 1. Shen, Y., Tian, B., Zhou, T.Y.: Studies on an extended (3+1)-dimensional variable-coefficient shallow water wave equation: Bilinear...
  • 2. Gao, X.Y., Guo, Y.J., Shan, W.R.: Shallow-water investigations: Bilinear auto-Bäcklund transformations for a (3+1)-dimensional generalized...
  • 3. Shan, H.W., Tian, B., Gao, X.T., Liu, H.D.: Lie-symmetry analysis, optimal system, analytic solutions, nonlinear self-adjointness and conservation...
  • 4. Liu, H.D., Tian, B., Cheng, C.D., Zhou, T.Y., Gao, X.T.: N-soliton, Hth-order breather, hybrid and multi-pole solutions for a variable-coefficient...
  • 5. Feng, C.H., Tian, B., Gao, X.T.: Bilinear Bäcklund transformations, as well as N-soliton, breather, fission/fusion and hybrid solutions...
  • 6. Gao, X.Y., Chen, X.Q., Guo, Y.J., Shan,W.R.: Cosmic-plasma environment, singular manifold and symbolic computation for a variable-coefficient...
  • 7. Gao, X.Y.: Symbolic computation on a (2+1)-dimensional generalized nonlinear evolution system in fluid dynamics, plasma physics, nonlinear...
  • 8. Nemirovskii, S.: On the dependence of thermodynamic variables on the relative velocity vns in a superfluid counterflowing helium. Phys....
  • 9. Celik, E.: Travelling wave solutions of a time regularised long wave equation associated with the Korteweg-de Viries equation in fluid...
  • 10. Geethalakshmi, V., Ravi Kumar, R., Kalarani, M.K., Karthikeyan, R., Sivakumar, R., Sathyamoorthy, N.K., Dheebakaran, G.: Stability of...
  • 11. Badshah, F., Tariq, K.U., Ilyas, H., Tufail, R.N.: Soliton, lumps, stability analysis and modulation instability for an extended (2+1)-dimensional...
  • 12. Yasmin, H., Alyousef, H.A., Asad, S., Khan, I., Matoog, R.T., El-Tantawy, S.A.: The Riccati-Bernoulli sub-optimal differential equation...
  • 13. Wang, Y., Lü, X., Ma, W.X.: Integrability characteristics and exact solutions of an extended (3+1)- dimensional variable-coefficient...
  • 14. Gao, X.Y.: Open-ocean shallow-water dynamics via a (2+1)-dimensional generalized variablecoefficient Hirota-Satsuma-Ito system: Oceanic...
  • 15. Wang, Y.H., Wang, H.: Nonlocal symmetry, CRE solvability and soliton-cnoidal solutions of the (2+1)- dimensional modified KdV-Calogero-Bogoyavlenkskii-Schiff...
  • 16. Feng, C.H., Tian, B., Gao, X.T.: Bilinear Bäcklund transformation, fission/fusion and periodic waves of a (3+1)-dimensional Kadomtsev-Petviashvili...
  • 17. Liu, H.D., Tian, B., Cheng, C.D., Zhou, T.Y., Gao, X.T., Shan, H.W.: Integrability and analytic solutions for a damped variable-coefficient...
  • 18. Huang, Y.H., Guo, R.: Wave breaking, dispersive shock wave, and phase shift for the defocusing complex modified KdV equation. Chaos 34,...
  • 19. Shan, H.W., Tian, B., Cheng, C.D., Gao, X.T., Chen, Y.Q., Liu, H.D.: N-soliton and other analytic solutions for a (3 + 1)-dimensional...
  • 20. Singh, S., Ray, S.S.: Painlevé integrability and analytical solutions of variable coefficients negative order KdV-Calogero-Bogoyavlenskii-Schiff...
  • 21. Wazwaz, A.M.: Two new Painlevé integrable KdV-calogero-Bogoyavlenskii-Schiff (KdV-CBS) equation and new negative-order KdV-CBS equation....
  • 22. Ali, K.K., Yilmazer, R., Osman, M.S.: Dynamic behavior of the (3+1)-dimensional KdV-CalogeroBogoyavlenskii-Schiff equation. Opt. Quantum...
  • 23. Wazwaz, A.M.: A variety of completely integrable Calogero-Bogoyavlenskii-Schiff equations with time-dependent coefficients. Int. J. Numer....
  • 24. Lan, Z.Z.: Multiple soliton asymptotics in a spin-1 Bose-Einstein condensate. Chin. Phys. Lett. 41, 090501 (2024)
  • 25. Yuan, W.X., Guo, R.: Physics-guided multistage neural network: A physically guided network for step initial values and dispersive shock...
  • 26. Liu, Y.H., Guo, R., Zhang, J.W.: Inverse scattering transform for the discrete nonlocal PT symmetric nonlinear Schrödinger equation with...
  • 27. Chen, Y., Lü, X., Jia, X.J., Tian, H.: Barrier option pricing and volatility surface predicting with an extended physics-informed neural...
  • 28. Guo, M.H., Lü, X., Jin, Y.X.: Extraction and reconstruction of variable-coefficient governing equations using Res-KAN integrating sparse...
  • 29. Chen, Y.Q., Wu, Z.T., Xiao, P.Y., Xiao, W.D., Liu, W.J.: Application of femtosecond mode-locked SnTe thin films and generation of bound-state...
  • 30. Xing, X.W., Liu, Y.X., Han, J.F., Liu, W.J., Wei, Z.Y.: Preparation of high damage threshold device based on Bi2Se3 film and its application...
  • 31. Liu, W.J., Xiong, X.L., Liu, M.L., Xing, X.W., Chen, H.L., Ye, H., Han, J.F., Wei, Z.Y.: Bi4Br 4-based saturable absorber with robustness...
  • 32. Liu, F.Y., Zhou, Q.: Two-component stripe soliton states in spin-1/2 spin-orbit-coupled Bose-Einstein condensates. Phys. D 472, 134540...
  • 33. Liu, F.Y., Zhou, Q.: Oscillatory soliton pairs in spin-orbit coupled spin-1/2 Bose-Einstein condensates. New J. Phys. 27, 023019 (2025)
  • 34. Ding, C.C., Zhou, Q., Malomed, B.A.: Beating stripe solitons arising from helicoidal spin-orbit coupling in Bose-Einstein condensates....
  • 35. Feng, C.H., Tian, B., Yang, D.Y., Gao, X.T.: Bilinear form, bilinear Bäcklund transformations, breather and periodic-wave solutions for...
  • 36. Feng, C.H., Tian, B., Gao, X.T.: Bilinear form, N solitons, breathers and periodic waves for a (3+1)- dimensional Korteweg-de Vries...
  • 37. Chen, Y.Q., Wu, Z.T., Xiao, P.Y., Xiao, W.D., Liu, W.J.: Application of femtosecond mode-locked SnTe thin films and generation of bound-state...
  • 38. Wang, Y., Lü, X., Ma, W.X.: Integrability characteristics and exact solutions of an extended (3 + 1)-dimensional variable-coefficient...
  • 39. Gao, X.Y., Liu, J.G., Wang, G.W.: Inhomogeneity, magnetic auto-Bäcklund transformations and magnetic solitons for a generalized variable-coefficient...
  • 40. Hirota, R.: The Direct Method in Soliton Theory. Cambridge Univ. Press, New York (2004)
  • 41. Gao, X.Y.: Hetero-Bäcklund transformation, bilinear forms and multi-solitons for a (2+1)-dimensional generalized modified dispersive...
  • 42. Clarkson, P.A., Kruskal, M.D.: New similarity reductions of the Boussinesq equation. J. Math. Phys. 30, 2201 (1989)
  • 43. Gao, X.Y.: In an ocean or a river: bilinear auto-Bäcklund transformations and similarity reductions on an extended time-dependent (3+1)-dimensional...
  • 44. Lou, S.Y., Ma, H.C.: Non-Lie symmetry groups of (2+1)-dimensional nonlinear systems obtained from a simple direct method. J. Phys....
  • 45. D. Zwillinger and V. Dobrushkin, Handbook of Differential Equations, 4th ed., Chapman & Hall/CRC, Boca Raton, FL (2022) DOI: https://doi.org/10.1201/9780429286834