Lie Symmetry Analysis of Fractional Kersten–Krasil’shchik Coupled KdV–mKdV System

• Panpan Wang ^[1] ; Xiufang Feng ^[1] ; Shangqin He ^[2]
  1. [1] Ningxia University

     Ningxia University

     China

     
  2. [2] North Minzu University
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 1, 2025
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • This paper investigates the invariance properties of the fractional Kersten– Krasil’shchik coupled KdV–mKdV system. By extending Lie symmetry analysis method to a fractional system, two vector fields are derived. The similarity transformation elegantly reduces the fractional system to a set of ordinary differential equations. Furthermore, the explicit power series solutions for the system are derived by employing the power series theory. Lastly, conservation laws for the system are established utilizing Ibragimov’s method.

• Referencias bibliográficas
  • 1. Goswami, A., Sushila, Singh, J., Kumar, D.: Numerical computation of fractional Kersten– Krasil’shchik coupled KdV–mKdV system occurring...
  • 2. Shah, N.A., Seikh, A.H., Chung, J.D.: The analysis of fractional-order Kersten–Krasil’shchik coupled KdV system, via a new integral transform....
  • 3. Sagar, B., Saha Ray, S.: Numerical solution of fractional Kersten–Krasil’shchik coupled KdV–mKdV system arising in shallow water waves....
  • 4. Jawarneh, Y., Yasmin, H., Ganie, A.H., Al-Sawalha, M.M., Ali, A.: Unification of adomian decomposition method and ZZ transformation for...
  • 5. Lie, S.: On integration of a class of linear partial differential equations by means of definite integrals. Arch. Math. 6(3), 328–368 (1881)
  • 6. Buckwar, E., Luchko, Y.: Invariance of a partial differential equation of fractional order under the lie group of scaling transformations....
  • 7. Gazizov, R.K., Kasatkin, A., Lukashchuk, S.Y.: Continuous transformation groups of fractional differential equations. Vestn. Usatu 9(3),...
  • 8. Gazizov, R., Kasatkin, A., Lukashchuk, S.Y.: Symmetry properties of fractional diffusion equations. Phys. Scr. 2009(T136), 014016 (2009)
  • 9. Akbulut, A., Ta¸scan, F.: Lie symmetries, symmetry reductions and conservation laws of time fractional modified Korteweg-de Vries (mkdv)...
  • 10. Akbulut, A., Almusawa, H., Kaplan, M., Osman, M.S.: On the conservation laws and exact solutions to the (3+1)-dimensional modified...
  • 11. Akbulut, A., Kaplan, M., Kumar, D., Ta¸scan, F.: The analysis of conservation laws, symmetries and solitary wave solutions of Burgers–Fisher...
  • 12. Liu, J., Geng, F.: An explanation on four new definitions of fractional operators. Acta Math. Sci. 44(4), 1271–1279 (2024)
  • 13. Liu, J., Yang, X., Feng, Y., Geng, L.: Invariant analysis and conservation laws for the space-time fractional kdv-like equation. Computation...
  • 14. Zhu, H., Zheng, J., Zhang, Z.: Approximate symmetry of time-fractional partial differential equations with a small parameter. Commun....
  • 15. Zhang, Z.: Symmetry determination and nonlinearization of a nonlinear time-fractional partial differential equation. P. Roy. Soc. A 476(2233),...
  • 16. Zhang, Z.-Y., Zheng, J.: Symmetry structure of multi-dimensional time-fractional partial differential equations. Nonlinearity 34(8), 5186...
  • 17. Jumarie, G.: Modified Riemann-Liouville derivative and fractional Taylor series of nondifferentiable functions further results. Comput....
  • 18. Gulsen, S., Inc, M.: Time fractional super KdV equation: Lie point symmetries, conservation laws, explicit solutions with convergence...
  • 19. Gu, Q., Wang, L.: Group classification, symmetry reductions and exact solutions of the time-fractional generalized thin film equation...
  • 20. Zhu, H., Zhang, Z., Zheng, J.: The time-fractional (2+1)-dimensional Hirota–Satsuma–Ito equations: Lie symmetries, power series solutions...
  • 21. Ibragimov, N.H.: A new conservation theorem. J. Math. Anal. Appl. 333(1), 311–328 (2007)
  • 22. Ibragimov, N.H., Avdonina, E.D.: Nonlinear self-adjointness, conservation laws, and the construction of solutions of partial differential...