Ir al contenido

Documat

Dynamics of Advanced Soliton Wave Profiles in a Nonlinear Model with Some Structural Behavior: Chaos Theory and Sensitivity Analysis

  • Umair Asghar [1] ; Muhammad Imran Asjad [2] ; Sachin Kumar [3] ; Suhad Ali Osman Abdallah [4]
    1. [1] University of Lahore

      University of Lahore

      Pakistán

    2. [2] University of Management and Technology

      University of Management and Technology

      Estados Unidos

    3. [3] University of Delhi

      University of Delhi

      India

    4. [4] King Khalid University

      King Khalid University

      Arabia Saudí

    Mostrar afiliaciones +
  • Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 4, 2025
  • Idioma: inglés
  • Enlaces
  • Resumen

    • In this article, we employ two advanced analytical techniques, the Modified Khater method (MKhat) and Nucci’s direct reduction technique to analyze the Konopelchenko–Dubrovsky equations for the first time. These methods yield novel analytical solutions, previously unexplored in the literature, for a class of integrable systems highly valuable for theoretical and mathematical investigations. Our study generates several new soliton solutions, including those involving trigonometric, periodic, exponential, and elliptic functions, as well as unique forms such as periodic solutions, cusped decay solitary solutions, stumpon solutions, peakon solutions, and kink-type solutions. The innovative application of these techniques not only simplifies the resolution of integrable systems but also provides efficient approaches for deriving soliton solutions, enhancing our understanding of the Konopelchenko–Dubrovsky equations. The results underscore the importance of exploring diverse wave phenomena across various scientific domains. Applications include ocean engineering, where wave dynamics and interactions in shallow and deep waters are studied; nonlinear optics, particularly in modeling optical solitons in fiber systems with dispersive and nonlinear effects; plasma physics, investigating plasma wave behaviors and charged particle interactions; and condensed matter physics, exploring solitonic structures in crystal lattices and other complex systems. To provide physical insights and better visual understanding, Mathematica software is used to create graphical representations of the solutions, including 3D, 2D, and contour plots. Additionally, chaos and sensitivity analyses are performed to investigate the dynamic aspects of the governing model, with periodic and quasi-periodic trajectory plots offering a deeper understanding of the system’s behavior. The Konopelchenko–Dubrovsky equations are well-regarded for modeling nonlinear wave phenomena in diverse physical contexts.

      This study not only highlights the broader significance of the model but also makes a significant contribution to the field, offering impactful results that pave the way for future advancements in related research areas.

  • Referencias bibliográficas
    • 1. Bhavna, P., A. K., Singh, S.: Transverse spectral instabilities in Konopelchenko-Dubrovsky equation. Stud. Appl. Math. 151(3), 1053–1071...
    • 2. Chai, X., Zhang, Y.: The φ dressing method for the (2+1)-dimensional Konopelchenko-Dubrovsky equation. Appl. Math. Lett. 134, 108378...
    • 3. El-Dessoky, M.M., Elmandouh, A.: Qualitative analysis and wave propagation for Konopelchenko- Dubrovsky equation. Alex. Eng. J. 67, 525–535...
    • 4. Kumar, S., Kaur, L., Niwas, M.: Some exact invariant solutions and dynamical structures of multiple solitons for the (2+1)-dimensional...
    • 5. Rani, S., Kumar, S.: Dynamics of Soliton Solutions and Various Evolving Formations of the Jaulent- Miodek and Zakharov-Kuzetsov Equations...
    • 6. Kumar, S., Rani, S., Mann, N.: Analytical Soliton Solutions to a (2 + 1)-Dimensional Variable Coefficients Graphene Sheets Equation...
    • 7. Rani, S., Kumar, S., Kumar, R.: Dynamical study of newly created analytical solutions, bifurcation analysis, and chaotic nature of the...
    • 8. Hussain, A., Ibrahim, T.F., Birkea, F.M.O., Al-Sinan, B.R.: Dynamical behavior of analytical soliton solutions to the Kuralay equations...
    • 9. Abbas, N., Hussain, A., Waseem Akram, M., Muhammad, S., Shuaib, M.: Invariant analysis of the multidimensional Martinez Alonso-Shabat equation....
    • 10. Abbas, N., Hussain, A., Muhammad, S., Shuaib,M., Herrera, J.: Lie symmetry analysis, travelingwave solutions and conservation laws of...
    • 11. Hussain, A., Ali, H., Zaman, F.D., Abbas, N.: A diverse variety of exact solutions for some nonlinear models via the G G -expansion method....
    • 12. Hussain, A., Ibrahim, T.F., Birkea, F.O., Alotaibi, A.M., Al-Sinan, B.R., Mukalazi, H.: Exact solutions for the Cahn-Hilliard equation...
    • 13. Khater, M.M.: Numerous accurate and stable solitary wave solutions to the generalized modified Equal-Width equation. Int. J. Theor. Phys....
    • 14. Khater, M.M.: Characterizing shallow water waves in channels with variable width and depth; computational and numerical simulations. Chaos,...
    • 15. Khater,M.M.: Horizontal stratification of fluids and the behavior of longwaves. The European Physical Journal Plus 138(8), 715 (2023)
    • 16. Khater, M.M.: Soliton propagation under diffusive and nonlinear effects in physical systems;(1+ 1)– dimensional MNW integrable equation....
    • 17. Khater, M.M.: Computational simulations of propagation of a tsunami wave across the ocean. Chaos, Solitons & Fractals 174, 113806...
    • 18. Kumar, S., Dhiman, S.K.: Analyzing specific waves and various dynamics of multi-peakons in (3+1)- dimensional p-type equation using...
    • 19. Kukkar, A.,Kumar, S.: Dynamic behavior of dark and bright solitons with analytical solutions, together with other soliton forms in the...
    • 20. Khater, M.M.: Advanced computational techniques for solving the modified KdV-KP equation and modeling nonlinear waves. Opt. Quant. Electron....
    • 21. Ali, K.K., Yusuf, A., Yokus, A., Ali, M.R.: Optical waves solutions for the perturbed Fokas-Lenells equation through two different methods....
    • 22. Hendy, A.S., Zaky, M.A., De Staelen, R.H.: A general framework for the numerical analysis of high-order finite difference solvers for...
    • 23. Zaky, M.A.: An accurate spectral collocation method for nonlinear systems of fractional differential equations and related integral equations...
    • 24. Jhangeer, A., Beenish, T., A. M., Ansari, A. R., Imran, M.: Analytical and dynamical analysis of nonlinear Riemann wave equation in plasma...
    • 25. Raza, N., Jhangeer, A., Amjad, Z., Rani, B., Muhammad, T.:Analyzing coupled-wave dynamics: lump, breather, two-wave and three-wave interactions...
    • 26. Jhangeer, A.: Ferroelectric frontiers: Navigating phase portraits, chaos, multistability and sensitivity in thin-film dynamics. Chaos,...
    • 27. Infal, B., Jhangeer, A., Muddassar, M.: Dynamical patterns in stochastic φ−4 equation: An analysis of quasi-periodic, bifurcation, chaotic...
    • 28. Malik, S., Hashemi, M.S., Kumar, S., Rezazadeh, H., Mahmoud,W., Osman,M.S.: Application of new Kudryashov method to various nonlinear...
    • 29. Osman, M.S., Almusawa, H., Tariq, K.U., Anwar, S., Kumar, S., Younis, M., Ma, W.X.: On global behavior for complex soliton solutions of...
    • 30. Kai,Y.,Chen, S., Zhang, K.,Yin, Z.: Exact solutions and dynamic properties of a nonlinear fourth-order time-fractional partial differential...
    • 31. Raza, N., Abdullah, M., Butt, A.R., Murtaza, I.G., Sial, S.: New exact periodic elliptic wave solutions for extended quantum Zakharov-Kuznetsov...
    • 32. Wang, K.J., Wang, G.D., Shi, F.: Diverse optical solitons to the Radhakrishnan–Kundu–Lakshmanan equation for the light pulses. Journal...
    • 33. Asghar, U., Asjad,M.I., Faridi,W.A., Muhammad, T.: The conserved vectors and solitonic propagating wave patterns formation with Lie symmetry...
    • 34. Raza, N., Kaplan, M., Javid, A., Inc, M.: Complexiton and resonant multi-solitons of a (4+ 1)- dimensional Boiti–Leon–Manna–Pempinelli...
    • 35. Khater, M.: Dynamics of Nonlinear Time Fractional Equations in ShallowWaterWaves. Int. J. Theor. Phys. 63(4), 1–12 (2024)
    • 36. Arshed, S., Raza, N., Javid, A., Baskonus, H.M.: Chiral solitons of (2+ 1)-dimensional stochastic chiral nonlinear Schrödinger equation....
    • 37. Kumari, P., Gupta, R.K., Kumar, S.: Non-auto-Bäcklund transformation and novel abundant explicit exact solutions of the variable coefficients...
    • 38. Rizvi, S.T.R., Khan, S.U.D., Hassan, M., Fatima, I.,Khan, S.U.D.: Stable propagation of optical solitons for nonlinear Schrödinger equation...
    • 39. Bashir, A., Seadawy, A.R., Rizvi, S.T.R., Younis, M., Ali, I., Abd Allah, A.M.: Application of scaling invariance approach, P-test and...
    • 40. Wang, K.J., Li, S.: Novel complexiton solutions to the new extended (3+ 1)-dimensional Boiti-Leon- Manna-Pempinelli equation for incompressible...
    • 41. Wang, K.J., Shi, F., Li, S., Li, G., Xu, P.: Resonant Y-type soliton, interaction wave and other wave solutions to the (3+ 1)-dimensional...
    • 42. Wang, K.J.: The generalized (3+ 1)-dimensional B-type Kadomtsev-Petviashvili equation: resonant multiple soliton, N-soliton, soliton...
    • 43. Wang, K.J.: N-soliton, solitonmolecules, Y-type soliton, periodic lump and other wave solutions of the newreduced B-type Kadomtsev-Petviashvili...
    • 44. Wang, K.J., Liu, J.H.: Mathematical model and the solution of the capillary vibration in a nanoscale deformable. Mathematical Methods...
    • 45. Srivastava, H.M., Baleanu, D., Machado, J.A.T., Osman, M.S., Rezazadeh, H., Arshed, S., Günerhan, H.: Traveling wave solutions to nonlinear...
    • 46. Tarla, S., Ali, K.K., Sun, T.C., Yilmazer, R., Osman, M.S.: Nonlinear pulse propagation for novel optical solitons modeled by Fokas system...
    • 47. Mao, J.J., Tian, S.F., Xu, T.Z., Shi, L.F.: Inverse scattering transforms of the inhomogeneous fifth-order nonlinear Schrödinger equation...
    • 48. Tala-Tebue, E., Korkmaz, A., Rezazadeh, H., Raza, N.: New auxiliary equation approach to derive solutions of fractional resonant Schrödinger...
    • 49. Khater, M.M.: Dynamical characterization of the wave’s propagation of optical pulses in monomode fibers. Int. J. Mod. Phys. B 38(11),...
    • 50. Khater, M.M.: Exploring the rich solution landscape of the generalized Kawahara equation: insights from analytical techniques. The European...
    • 51. Khater, M.M.: Novel constructed dark, bright and rogue waves of three models of the well-known nonlinear Schrödinger equation. Int. J....
    • 52. Khater,M.M.: Physical and dynamic characteristics of high-amplitude ultrasonic wave propagation in nonlinear and dissipative media. Mod....
    • 53. El-Dessoky, M.M., Elmandouh, A.: Qualitative analysis and wave propagation for Konopelchenko- Dubrovsky equation. Alex. Eng. J. 67, 525–535...
    • 54. Gu, Y., Manafian, J., Malmir, S., Eslami, B., Ilhan, O.A.: Lump, lump-trigonometric, breather waves, periodic wave and multi-waves solutions...
    • 55. Hussain, A., Parveen, T., Younis, B.A., Ahamd, H.U., Ibrahim, T.F., Sallah, M.: Dynamical behavior of solitons of the (2+ 1)-dimensional...
    • 56. Saha Ray, S., Sagar, B.: Numerical soliton solutions of fractional modified (2+ 1)-dimensional Konopelchenko-Dubrovsky equations in...
    • 57. Ma, H., Bai, Y., Deng, A.: Multiple lump solutions of the (2+ 1)-dimensional Konopelchenko- Dubrovsky equation. Mathematical Methods...
    • 58. Khater, M.M.: An integrated analytical-numerical framework for studying nonlinear PDEs: The GBF case study. Mod. Phys. Lett. B 39(20),...
    • 59. Ashraf, F., Ashraf, R., Akgül, A.: Traveling waves solutions of Hirota-Ramani equation by modified extended direct algebraic method and...
    • 60. Jhangeer, A., Ansari, A.R., Imran, M.,Riaz, M.B.,Talafha, A.M.: Application of propagating solitons to Ivancevic option pricing governing...
    • 61. Hashemi, M.S., Mirzazadeh, M.: Exact solutions of nonlinear stochastic Newell-Whitehead-Segel equation by a reduction technique. The European...
    • 62. Seadawy, A.R., Yaro, D., Lu, D.: Propagation of nonlinear waves with a weak dispersion via coupled (2+ 1)-dimensional Konopelchenko-Dubrovsky...
    • 63. Barman, H.K., Akbar, M.A., Osman, M.S., Nisar, K.S., Zakarya, M., Abdel-Aty, A.H., Eleuch, H.: Solutions to the Konopelchenko-Dubrovsky...
    • 64. Kumar, S., Mann, N., Kharbanda, H., Inc, M.: Dynamical behavior of analytical soliton solutions, bifurcation analysis, and quasi-periodic...
    • 65. Arafat, S.Y., Rahman,M.M., Karim, M.F.,Amin, M.R.:Wave profile analysis of the (2+ 1)-dimensional Konopelchenko-Dubrovsky model in...
    • 66. Dong, M.J., Tian, L.X., Shi, W.,Wei, J.D., Wang, Y.: Solitons, breathers and rational solutions for the (2+ 1)-dimensional Konopelchenko-Dubrovsky...
    • 67. Rafiq,M.H., Jhangeer, A., Raza, N.: Symmetry and complexity: A Lie symmetry approach to bifurcation, chaos, stability and travelling wave...
    • 68. Wang, K.J.,Wang, G.D., Shi, F., Liu, X.L., Zhu, H.W.: Variational principle, Hamiltonian, bifurcation analysis, chaotic behaviors and...
    • 69. Wang, K.J., Liu, X.L., Shi, F., Li, G.: Bifurcation and sensitivity analysis, chaotic behaviors, variational principle, Hamiltonian and...
    • 70. Liang, Y.H.,Wang, K.J.: Bifurcation analysis, chaotic phenomena, variational principle, Hamiltonian, solitary and periodic wave solutions...
Fundación Dialnet

Mi Documat

Opciones de artículo

Opciones de compartir

Opciones de entorno