A New Composite Technique to Obtain Non-traveling Wave Solutions of the (2+1)-dimensional Extended Variable Coefficients Bogoyavlenskii–Kadomtsev–Petviashvili Equation

• Xiaoxiao Zheng ^[1] ; Lingling Zhao ^[1] ; Yuanqing Xu ^[2]
  1. [1] Qufu Normal University

     Qufu Normal University

     China

     
  2. [2] Beijing University of Technology

     Beijing University of Technology

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 22, Nº 2, 2023
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • In this article, we investigate non-traveling wave solutions for the (2+1)-dimensional extended variable coefficients Bogoyavlenskii–Kadomtsev–Petviashvili equation with time-dependent coefficients (VC-BKP). Inspired by Shang, we apply the extended three-wave method and the generalized variable separation method to the investigated problem for the first time in this article. The technique is effective, easily applicable, and reliable in solving non-traveling wave solutions. We successfully obtain forty-four exact non-traveling solutions, including double periodic solutions, kinky breather wave solution, periodic cross-kink solution and some new exact non-traveling solutions obtained firstly in this paper. These results all have a tail which gives a prediction of physical phenomenon. Moreover, we discuss the arbitrary coefficients of solutions in the real, purely imaginary and complex domains, which greatly enriches the forms of solutions. The dynamic phenomena of four types of exact solutions are demonstrated by contour, 2D and 3D graphics, which help to show their physical interpretation.

• Referencias bibliográficas
  • 1. Xie, X.Y., Tian, B., Sun, W.R., et al.: Solitary wave and multi-front wave collisions for the Bogoyavlenskii–Kadomtsev–Petviashili equation...
  • 2. Zhao, Z.L., He, L.C., Wazwaz, A.M.: Dynamics of lump chains for the BKP equation describing propagation of nonlinear waves. Chinese Phys....
  • 3. Yin, H.M., Tian, B., Zhen, H.L., et al.: Solitons, bilinear Bäcklund transformations and conservation laws for a (2+1)-dimensional...
  • 4. Wang, C.J., Fang, H.: Non-auto Bäclund transformation, nonlocal symmetry and CRE solvability for the Bogoyavlenskii–Kadomtsev–Petviashvili...
  • 5. Wang, C.J., Fang, H.: Bilinear Bäcklund transformations, kink periodic solitary wave and lump wave solutions of the Bogoyavlenskii–Kadomtsev–Petviashvili...
  • 6. Xia, P., Zhang, Y., Zhang, H.Y., Zhuang, Y.D.: Rogue lumps on a background of kink waves for the Bogoyavlenskii–Kadomtsev–Petviashvili...
  • 7. Rui, W.J., Zhang, Y.F.: Soliton and lump-soliton solutions in the Grammian form for the Bogoyavlenskii–Kadomtsev–Petviashvili equation....
  • 8. Moretlo, T.S., Adem, A.R., Muatjetjeja, B.: A generalized (1+2)-dimensional Bogoyavlenskii–Kadomtsev–Petviashvili (BKP) equation: multiple...
  • 9. Zhao, Z.L., Yue, J., He, L.C.: New type of multiple lump and rogue wave solutions of the (2+1)-dimensional Bogoyavlenskii–Kadomtsev–Petviashvili...
  • 10. Wazwaz, A.M.: On integrability of an extended Bogoyavlenskii–Kadomtsev–Petviashvili equation: multiple soliton solutions. Int. J. Numer....
  • 11. Mabenga, C., Muatjetjeja, B., Motsumi, T.G.: Similarity reductions and conservation laws of an extended Bogoyavlenskii–Kadomtsev–Petviashvili...
  • 12. El-Shiekh, R.M.: Jacobi elliptic wave solutions for two variable coefficients cylindrical Korteweg-de Vries models arising in dusty plasmas...
  • 13. El-Shiekh, R.M., Gaballah, M.: Integrability, similarity reductions and solutions for a (3+1)-dimensional modified Kadomtsev–Petviashvili...
  • 14. Ma, W.X.: N-soliton solutions and the Hirota conditions in (2+1)-dimensions. Opt. Quant. Electron. 52, 511 (2020)
  • 15. Lan, Z.Z.: Multi-soliton solutions for a (2+1)-dimensional variable-coefficient nonlinear Schrödinger equation. Appl. Math. Lett....
  • 16. Xin, X.P., Zhang, L.L., Xia, Y.R., Liu, H.Z.: Nonlocal symmetries and exact solutions of the (2+1)-dimensional generalized variable...
  • 17. El-Shiekh, R.M.: Novel solitary and shock wave solutions for the generalized variable-coefficients (2+1)-dimensional KP-Burger equation...
  • 18. Gao, X.Y., Guo, Y.J., Shan, W.R., et al.: Magnetooptic studies on a ferromagnetic material via an extended (3+1)-dimensional variable-coefficient...
  • 19. Silem, A., Lin, J.: Exact solutions for a variable-coefficients nonisospectral nonlinear Schrödinger equation via Wronskian technique....
  • 20. Yan, X.Y., Liu, J.Z., Yang, J.J., Xin, X.P.: Lie symmetry analysis, optimal system and exact solutions for variable-coefficients (2+1)-dimensional...
  • 21. Guo, S.M., Mei, L.Q., Zhou, Y.B.: The compound (G /G)-expansion method and double non-traveling wave solutions of (2+1)-dimensional...
  • 22. Zheng, B.L., Kai, Y., Xu, W.L., et al.: Exact traveling and non-traveling wave solutions of the time fractional reaction-diffusion equation....
  • 23. Lv, L.B., Shang, Y.D.: Abundant new non-travelling wave solutions for the (3+1)-dimensional potentialYTSF equation. Appl. Math. Lett....
  • 24. Shang, Y.D.: Abundant explicit non-traveling wave solutions for the (2+1)-dimensional breaking soliton equation. Appl. Math. Lett....
  • 25. Xu, Y.Q., Zheng, X.X., Xin, J.: New non-traveling wave solutions for the (2+1)-dimensional variable coefficients Date-Jimbo–Kashiwara–Miwa...