Ir al contenido

Documat

Dynamical Study of Newly Created Analytical Solutions, Bifurcation Analysis, and Chaotic Nature of the Complex Kraenkel–Manna–Merle System

  • Setu Rani [1] ; Sachin Kumar [1] ; Raj Kumar [1]
    1. [1] University of Delhi

      University of Delhi

      India

  • Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº Extra 1, 2024
  • Idioma: inglés
  • DOI: 10.1007/s12346-024-01148-z
  • Enlaces
  • Resumen

    • The present research explores the analytical solutions and dynamics of complex Kraenkel–Manna–Merle system, which are exploited in ceramic-like materials with magnetic characteristics in electronics. Two distinct approaches, the extended sinh-Gordon equation expansion and the modified auxiliary equation are employed to derive soliton solutions in various function forms, including hyperbolic, trigonometric, rational, and Jacobi elliptic functions. The stability and accuracy of these solutions are confirmed through modulation instability analysis. Several specific solutions are illustrated through numerical simulations after assigning values to the free parameters. By back-substituting into the original model, the newly generated solutions confirm the validity of the new findings and ensure their accuracy. The obtained multiple soliton solutions show that the two approaches are effective, efficient, reliable, and potent for studying nonlinear evolution equations. Furthermore, a transformation converted the system into a planar dynamical system, allowing phase portraits to be analyzed. Moreover, the introduction of a perturbed term uncovered chaotic behavior across a range of parameter values, illustrated through both two-dimensional and three-dimensional graphics. The study presents novel analytical solutions that offer insights into nonlinear short wave interactions, which have not been previously documented using these methodologies.

  • Referencias bibliográficas
    • 1. Wazwaz, A.-M.: Extended (3 + 1)-dimensional Kairat-II and Kairat-X equations: Painlevé integrability, multiple soliton solutions, lump...
    • 2. Ma, W.X., Zhou, Y.: Lump solutions to nonlinear partial differential equations via Hirota bilinear forms. J. Differ. Equ. 264, 2633–2659...
    • 3. Kudryashov, N.A., Nifontov, D.R.: Exact solutions and conservation laws of the fourth-order nonlinear Schrödinger equation for the embedded...
    • 4. Kumar, S., Hamid, I.: New interactions between various soliton solutions, including bell, kink, and multiple soliton profiles, for the...
    • 5. Dhiman, S.K., Kumar, S.: Analyzing specific waves and various dynamics of multi-peakons in (3+1)- dimensional p-type equation using...
    • 6. Kumar, S., Mohan, B.: Bilinearization and new center-controlled N-rogue solutions to a (3+1)- dimensional generalized KdV-type equation...
    • 7. Kumar, S., Dhiman, S.K.: Exploring cone-shaped solitons, breather, and lump-forms solutions using the lie symmetry method and unified approach...
    • 8. Akinyemi, L., Veeresha, P., Darvishi, M.T., Rezazadeh, H., ¸Senol, M., Akpan, U.: A novel approach to study generalized coupled cubic Schrödinger-Korteweg-de...
    • 9. Seadawy, A.R.: Stability analysis for Zakharov-Kuznetsov equation of weakly nonlinear ion-acoustic waves in a plasma. Comput. Math. Appl....
    • 10. Seadawy, A.R., Rizvi, S.T.R., Ali, I., Younis, M., Ali, K., Makhlouf, M.M., Althobaiti, A.: Conservation laws, optical molecules, modulation...
    • 11. Seadawy, A.R., Arshad, M., Lu, D.: The weakly nonlinear wave propagation theory for the KelvinHelmholtz instability in magnetohydrodynamics...
    • 12. Kumar, S., Niwas, M.: Exploring lump soliton solutions and wave interactions using new Inverse (G /G)-expansion approach: applications...
    • 13. Jhangeer, A., Rezazadeh, H., Seadawy, A.: A study of travelling, periodic, quasiperiodic and chaotic structures of perturbed Fokas-Lenells...
    • 14. Rabie, W.B., Ahmed, H.M., Hashemi, M.S., Mirzazadeh, M., Bayram, M.: Generating optical solitons in the extended (3 + 1)-dimensional...
    • 15. Zhao, X., Zhi, H., Yu, Y., Zhang, H.: A new Riccati equation expansion method with symbolic computation to construct new travelling wave...
    • 16. Ntiamoah, D., Ofori-Atta, W., Akinyemi, L.: The higher-order modified Korteweg-de Vries equation: its soliton, breather and approximate...
    • 17. Alquran, M.: Optical bidirectional wave solutions to new two mode extension of the coupled KdVSchrödinger equations. Opt. Quant. Electron....
    • 18. Raza, N., Zubair, A.: Optical dark and singular solitons of generalized nonlinear Schrödinger’s equation with anti-cubic law of nonlinearity....
    • 19. Wazwaz, A.M.: Two new integrable fourth-order nonlinear equations: multiple soliton solutions and multiple complex soliton solutions....
    • 20. Seadawy, A.R., Alsaedi, B.A.: Soliton solutions of nonlinear Schrödinger dynamical equation with exotic law nonlinearity by variational...
    • 21. Seadawy, A.R., Alsaedi, B.: Contraction of variational principle and optical soliton solutions for two models of nonlinear Schrödinger...
    • 22. Mathanaranjan, T., Rezazadeh, H., Senol, M., Akinyemi, L.: Optical singular and dark solitons to the nonlinear Schrödinger equation in...
    • 23. Arshed, S., Raza, N., Alansari, M.: Soliton solutions of the generalized Davey-Stewartson equation with full nonlinearities via three...
    • 24. Raza, N., Arshed, S., Javid, A.: Optical solitons and stability analysis for the generalized second-order nonlinear Schrödinger equation...
    • 25. Raza, N., Arshed, S.: Chiral bright and dark soliton solutions of Schrödinger’s equation in (1+2)- dimensions. Ain Shams Eng. J. 11,...
    • 26. Ma, W.X., Osman, M.S., Arshed, S., Raza, N., Srivastava, H.M.: Practical analytical approaches for finding novel optical solitons in the...
    • 27. Akinyemi, L., Houwe, A., Abbagari, S., Wazwaz, A., Alshehri, H.M., Osman, M.S.: Effects of the higher-order dispersion on solitary waves...
    • 28. Zubair, A., Raza, N., Mirzazadeh, M., Liu, W., Zhou, Q.: Analytic study on optical solitons in paritytime-symmetric mixed linear and nonlinear...
    • 29. Kumar, S., Rani, S.: Invariance analysis, optimal system, closed-form solutions and dynamical wave structures of a (2+ 1)-dimensional...
    • 30. Rafiq, M.H., Jhangeer, A., Raza, N.: Symmetry and complexity: a Lie symmetry approach to bifurcation, chaos, stability and travelling...
    • 31. Raza, N., Jhangeer, A., Rahman, R.U., Butt, A.R., Chu, Y.M.: Sensitive visualization of the fractional Wazwaz-Benjamin-Bona-Mahony equation...
    • 32. Yang, X.L., Tang, J.S.: Travelling wave solutions for Konopelchenko-Dubrovsky equation using an extended sinh-Gordon equation expansion...
    • 33. Shen, Y., Tian, B., Zhou, T.Y., Cheng, C.D.: Complex Kraenkel-Manna-Merle system in a ferrite: n-fold Darboux transformation, generalized...
    • 34. Nguepjouo, F.T., Kuetche, V.K., Kofane, T.C.: Soliton interactions between multivalued localized waveguide channels within ferrites. Phys....
    • 35. Kamdem, B.A., Lemoula, R.K.K., Kuetche, V.K., Defo, J.J., Noule, R.S., Youssoufa, S.: Polarized waveguide excitations in microwave ferrites:...
    • 36. Lemoula, R.K.K., Kamdem, B.A., Kuetche, V.K., Noule, R.S., Defo, J.J., Youssoufa, S.: Kruskals simplification scheme in ferrite dynamics....
    • 37. Tchokouansi, H.T., Felenou, E.T., Kuetche, V.K., Tchidjo, R.T.: Dynamics of damped single valued magnetic wave in inhomogeneous circularly...
    • 38. Li, B.Q., Ma, Y.L.: Loop-like periodic waves and solitons to the Kraenkel-Manna-Merle system in ferrites. J. Electromagnet Waves Appl....
    • 39. Si, H.L., Li, B.Q.: Two types of soliton twining behaviors for the Kraenkel-Manna-Merle system in saturated ferromagnetic materials. Optik...
    • 40. Li, B.Q., Ma, Y.L.: Rich soliton structures for the Kraenkel-Manna-Merle (KMM) system in ferromagnetic materials. J. Supercond. Nov. Magn....
    • 41. Mahak, N., Akram, G.: The modified auxiliary equation method to investigate solutions of the perturbed nonlinear Schrödinger equation...
    • 42. Saha, M., Sarma, A.K.: Solitary wave solutions and modulation instability analysis of the nonlinear Schrödinger equation with higher order...
    • 43. Raza, N., Jhangeer, A., Arshed, S., Butt, A.R., Chu, Y.: Dynamical analysis and phase portraits of two-mode waves in different media....
    • 44. Kumar, S., Mann, N.: Dynamic study of qualitative analysis, traveling waves, solitons, bifurcation, quasiperiodic, and chaotic behavior...
    • 45. Perko, L.: Differential equations and dynamical systems. third edition, Texts in Applied Mathematics 7, Springer-Verlag, New York (2001)
    • 46. Rafiq, M.H., Raza, N., Jhangeer, A., Zidan, A.M.: Qualitative analysis, exact solutions and symmetry reduction for a generalized (2+1)-dimensional...
    • 47. Jhangeer, A., Raza, N., Ejaz, A., Rafiq, M.H., Baleanu, D.: Qualitative behavior and variant soliton profiles of the generalized P-type...
    • 48. Rafiq, M.H., Raza, N., Jhangeer, A.: Nonlinear dynamics of the generalized unstable nonlinear Schrödinger equation: a graphical perspective....
    • 49. Houwe, A., Abbagari, S., Akinyemi, L., Doka, S.Y., Metwally, A.S.M., Ahmad, H.: Bifurcation and chaotic patterns of the solitary waves...
Fundación Dialnet

Mi Documat

Opciones de artículo

Opciones de compartir

Opciones de entorno