Ir al contenido

Documat

Traveling Wave Solutions for Two Perturbed Nonlinear Wave Equations with Distributed Delay

  • Jundong Wang [4] ; Lijun Zhang [5] ; Xuwen Huo [1] ; Na Ma [2] ; Chaudry Masood Khalique [3]
    1. [1] Zhejiang Sci-Tech University

      Zhejiang Sci-Tech University

      China

    2. [2] Qingdao University of Science and Technology

      Qingdao University of Science and Technology

      China

    3. [3] North-West University

      North-West University

      Tlokwe City Council, Sudáfrica

    4. [4] Shandong University of Science and Technology & Qingdao University of Science and Technology
    5. [5] North-West University (Mafikeng Campus) & Shandong University of Science and Technology
    Mostrar afiliaciones +
  • Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº 4, 2024
  • Idioma: inglés
  • Enlaces
  • Resumen

    • Traveling wave solutions are a class of invariant solutions which are critical for shallow water wave equations. In this paper, traveling wave solutions for two perturbed KP-MEW equations with a local delay convolution kernel are examined. The model equation is reduced to a planar near-Hamiltonian system via geometric singular perturbation theorem, and the qualitative properties of the corresponding unperturbed system are analyzed by using dynamical system approach. The persistence of the bounded traveling wave solutions for the perturbed KP-MEW equations with delay is investigated. By using a criterion for the monotonicity of ratio of two Abelian integrals and Melnikov’s method, the existence of kink (anti-kink) wave solutions and periodic wave solutions of the model equation are established. The result shows that the delayed KP-MEW equations with positive perturbation and the one with negative perturbation exhibit completely diverse dynamical properties. These new findings greatly enrich the understanding of dynamical properties of the traveling wave solutions of perturbed nonlinear wave equations with local delay convolution kernel. Numerical experiments further confirm and illustrate the theoretical results.

  • Referencias bibliográficas
    • 1. Kadomtsev, B., Petviashvili, V.: On the stability of solitary waves in weakly dispersive media. Sov. Phys. Dokl. 15, 539–541 (1970)
    • 2. Chakravarty, S., Kodama, Y.: Soliton solutions of the KP equation and application to shallow water waves. Stud. Appl. Math. 123, 83–151...
    • 3. Zaki, S.I.: Solitary wave interactions for the modified equal width equation. Comput. Phys. Commun. 126, 219–231 (2000)
    • 4. Esen, A., Kutluay, S.: Solitary wave solutions of the modified equal width wave equation. Commun. Nonlinear Sci. Numer. Simul. 82, 1538–1546...
    • 5. Wazwaz, A.M.: The tanh method and the sine-cosine method for solving the KP-MEW equation. Int. J. Comput. Math. 82, 235–246 (2005)
    • 6. Seadawy, A.R., Iqbal, M., Lu, D.: Applications of propagation of long-wave with dissipation and dispersion in nonlinear media via solitary...
    • 7. Li, J., Dai, H.: On the study of singular nonlinear traveling wave equation: dynamical system approach. Science Press, Beijing (2007)
    • 8. Li, J.: Singular traveling wave equations: bifurcation and exact solutions. Science Press, Beijing (2013)
    • 9. Mahmud, A., Tanriverdi, T., Muhamad, K.: Exact traveling wave solutions for (2+1)-dimensional Konopelchenko-Dubrovsky equation by using...
    • 10. Han, M., Zhang, L., Wang, Y., et al.: The effects of the singular lines on the traveling wave solutions of modified dispersive water wave...
    • 11. Zhang, L., Chen, L.Q., Huo, X.: The effects of horizontal singular straight line in a generalized nonlinear Klein-Gordon model equation....
    • 12. Younas, U., Seadawy, A.R., Younis, M., et al.: Optical solitons and closed form solutions to the (3+1)- dimensional resonant Schrödinger...
    • 13. Seadawy, A.R., Rizvi, S.T.R., Ahmad, S., et al.: Lump, lump-one stripe, multiwave and breather solutions for the Hunter-Saxton equation....
    • 14. Seadawy, A.R.: Stability analysis for Zakharov-Kuznetsov equation of weakly nonlinear ion-acoustic waves in a plasma. Comput. Math. Appl....
    • 15. Rizvi, S.T.R., Seadawy, A.R., Ahmed, S., et al.: Study of multiple lump and rogue waves to the generalized unstable space time fractional...
    • 16. Jarad, F., Jhangeer, A., Awrejcewicz, J., Ahmed, S., et al.: Investigation of wave solutions and conservation laws of generalized Calogero-Bogoyavlenskii-Schiff...
    • 17. Hamza Rafiq, M., Jhangeer, A., Raza, N.: Symmetry and complexity: A Lie symmetry approach to bifurcation, chaos, stability and travelling...
    • 18. Kurkcu, H., Riaz, M.B., Imran, M., et al.: Lie analysis and nonlinear propagating waves of the (3+1)- dimensional generalized Boiti-Leon-Manna-Pempinelli...
    • 19. Rafiq, M.H., Raza, N., Jhangeer, A.: Nonlinear dynamics of the generalized unstable nonlinear Schrödinger equation: a graphical perspective....
    • 20. Chen, Y., Liu, Z.: The bifurcations of solitary and kink waves described by the Gardner equation. Discrete Cont. Dyn. S 9(6), 1629–1645...
    • 21. Zhang, L., Chen, G., Li, J.: Bifurcations and exact bounded solutions of some traveling wave systems determined by integrable nonlinear...
    • 22. Chen, A., Wen, S., Tang, S., et al.: Effects of quadratic singular curves in integrable equations. Stud. Appl. Math. 134(1), 24–61 (2015)
    • 23. Li, J., Qiao, Z.: Bifurcations and exact traveling wave solutions for a generalized Camassa-Holm equation. Int. J. Bifur. Chaos 23, 1350057–117...
    • 24. Yang, R., Kai, Y.: Dynamical properties, modulation instability analysis and chaotic behaviors to the nonlinear coupled Schrödinger equation...
    • 25. Ali, F., Jhangeer, A., Muddassar, M., et al.: Solitonic, quasi-periodic, super nonlinear and chaotic behaviors of a dispersive extended...
    • 26. Sardar, M., Khajanchi, S., Ahmad, B.: A tumor-immune interaction model with the effect of impulse therapy. Commun. Nonlinear Sci. Numer....
    • 27. Khajanchi, S., Nieto, J.J.: Spatiotemporal dynamics of a glioma immune interaction model. Sci. Rep. 11, 22385 (2021)
    • 28. Sarkar, K., Khajanchi, S., Mali, P.C.: A Delayed Eco-Epidemiological Model with Weak Allee Effect and Disease in Prey. Int. J. Bifur....
    • 29. Biswas, S., Ahmad, B., Khajanchi, S.: Exploring dynamical complexity of a cannibalistic ecoepidemiological model with multiple time delay....
    • 30. Khajanchi, S.: The impact of immunotherapy on a glioma immune interaction model. Chaos Soliton. Fract. 152, 111346 (2021)
    • 31. Fenichel, N.: Geometric singular perturbation theory for ordinary differential equations. J. Differ. Equ. 31, 53–98 (1979)
    • 32. Jones, C.K.R.T.: Geometric singular perturbation theory. Dyn. Syst. 1609, 44–118 (1995)
    • 33. Han, M.: Bifurcation theory of limit cycles. Science press, Beijing (2013)
    • 34. Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Springer-Verlag, New York (2000)
    • 35. Du, Z., Ren, Y., Lin, X.: Dynamics of solitary waves and periodic waves for a generalized KP-MEWBurgers equation with damping. Commun....
    • 36. Li, X., Du, Z., Ji, S.: Existence results of solitary wave solutions for a delayed Camassa-Holm-KP equation. Commun. Pur. Appl. Anal....
    • 37. Wang, J., Zhang, L., Li, J.: New solitary wave solutions of a generalized BBM equation with distributed delays. Nonlinear Dyn. 111, 4631–4643...
    • 38. Zhao, Z.: Solitary waves of the generalized KdV equation with distributed delays. J. Math. Anal. Appl. 344, 32–41 (2008)
    • 39. Ogawa, T.: Traveling wave solutions to a perturbed Korteweg-de Vries equation. Hiroshima Math. J. 24, 401–422 (1994)
    • 40. Zhang, L., Wang, J., Shchepakina, E., Sobolev, V.: New type of solitary wave solution with coexisting crest and trough for a perturbed...
    • 41. Sun, X., Huang, W., Cai, J.: Coexistence of the solitary and periodic waves in convecting shallow water fluid. Nonlinear Anal-Real 53,...
    • 42. Chen, A., Guo, L., Deng, X.: Existence of solitary waves and periodic waves for a perturbed generalized BBM equation. J. Differ. Equ....
    • 43. Zhu, K., Wu, Y., Shen, J., et al.: New solitary wave solutions in a perturbed generalized BBM equation. Nonlinear Dyn. 97, 2413–2423 (2019)
    • 44. Guo, L., Zhao, Y.: Existence of periodic waves for a perturbed quintic BBM equation. Discrete Cont. Dyn. Sys. 40, 4689–4703 (2020)
    • 45. Du, Z., Li, J., Li, X.: The existence of solitary wave solutions of delayed Camassa-Holm equation via a geometric approach. J. Funct....
    • 46. Wang, J., Yuen, M., Zhang, L.: Persistence of solitary wave solutions to a singularly perturbed generalized mKdV equation. Appl. Math....
    • 47. Wei, J., Tian, L., Zhou, J., Zhen, Z.: Existence, uniqueness and asymptotic behavior of traveling wave fronts for a generalized Fisher...
    • 48. Li, L., Yao, L.: Fault tolerant control of fuzzy stochastic distribution systems with packet dropout and time delay. IEEE T. Autom. Sci....
    • 49. Zhang, Z., Li, C.: Bifurcation Theory Foundation of Vector field. Higher Education Press, Beijing (1997). ((in chinese))
    • 50. Li, C., Zhang, Z.: A criterion for determining the monotonicity of the ratio of two Abelian integrals. J. Differ. Equ. 124, 407–424 (1996)
    • 51. Zhou, Y., Liu, Q., Zhang, W.: Bounded traveling waves of the generalized Burgers-Fisher equation. Int. J. Bifurcat. Chaos. 23(3), 1350054...
    • 52. Zhang, H., Xia, Y., Ngbo, P.R.: Global existence and uniqueness of a periodic wave solution of the generalized Burgers-Fisher equation....
Fundación Dialnet

Mi Documat

Opciones de artículo

Opciones de compartir

Opciones de entorno