Ir al contenido

Documat

Dynamics of General Soliton and Rational Solutions in the (3 + 1)-Dimensional Nonlocal Mel’nikov Equation with Non-zero Background

  • Xiaolin Yang [1] ; Yi Zhang [1] ; Wenjing Li [1]
    1. [1] Zhejiang Normal University

      Zhejiang Normal University

      China

  • Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº 5, 2024
  • Idioma: inglés
  • DOI: 10.1007/s12346-024-01068-y
  • Enlaces
  • Resumen

    • Employing the KP reduction approach, the primary goal of this research work is to investigate the soliton and rational solutions of the (3 + 1)-dimensional nonlocal Mel’nikov equation with non-zero background. The solutions presented are all N × N Gram determinants. In contrast to the previous exact solutions of the nonlocal model obtained by the KP reduction method, we introduce two types of parameter constraints into the τ function. This leads to the appearance of rational solutions and soliton (breather) solutions against a background of periodic wave. In particular, the soliton types we obtained are dark soliton, antidark soliton, breather, periodic wave and degenerate soliton. Furthermore, it has been discovered that lumps can appear in odd or even numbers in two backgrounds, which is a novel finding. The dynamic behavior of all solutions has been comprehensively analyzed.

  • Referencias bibliográficas
    • 1. Rizvi, S.T.R., Seadawy, A.R., Ahmed, S., Younis, M., Ali, K.: Study of multiple lump and rogue waves to the generalized unstable space...
    • 2. Ma, Y., Li, B.: Interaction behaviors between solitons, breathers and their hybrid forms for a short pulse equation. Qual. Theory. Dyn....
    • 3. Li, B., Ma, Y.: Higher-order breathers and breather interactions for the AB system in fluids. Eur. Phys. J. Plus 138, 475 (2023)
    • 4. Ma, Y., Li, B.: Higher-order hybrid rogue wave and breather interaction dynamics for the AB system in two-layer fluids. Math. Comput. Simul....
    • 5. Seadawy, A.R., Rizvi, S.T.R., Ali, I., Younis, M., Ali, K., Makhlouf, M.M., Althobaiti, A.: Conservation laws, optical molecules, modulation...
    • 6. Seadawy, A.R., Arshad, M., Lu, D.: The weakly nonlinear wave propagation theory for the KelvinHelmholtz instability in magnetohydrodynamics...
    • 7. Iqbal, M., Seadawy, A.R., Lu, D.: Applications of nonlinear longitudinal wave equation in a magnetoelectro-elastic circular rod and new...
    • 8. Seadawy, A.R., Lu, D., Iqbal, M.: Application of mathematical methods on the system of dynamical equations for the ion sound and Langmuir...
    • 9. Seadawy, A.R.: Stability analysis for Zakharov–Kuznetsov equation of weakly nonlinear ion-acoustic waves in a plasma. Comput. Math. Appl....
    • 10. Bender, C.M., Boettcher, S.: Real spectra in non-Hermitian Hamiltonians having PT symmetry. Phys. Rev. Lett. 80, 5243–5246 (1998)
    • 11. Ablowitz, M.J., Musslimani, Z.H.: Inverse scattering transform for the integrable nonlocal nonlinear Schrödinger equation. Nonlinearity...
    • 12. Feng, B., Luo, X., Ablowitz, M.J., Musslimani, Z.H.: General soliton solution to a nonlocal nonlinear Schrödinger equation with zero and...
    • 13. Ablowitz, M.J., Musslimani, Z.H.: Integrable space-time shifted nonlocal nonlinear equations. Phys. Lett. A 409, 127516 (2021)
    • 14. Yang, J.: General N-solitons and their dynamics in several nonlocal nonlinear Schrödinger equations. Phys. Lett. A 383, 328–337 (2019)
    • 15. Ye, R., Zhang, Y.: General soliton solutions to a reverse-time nonlocal nonlinear Schrödinger equation. Stud. Appl. Math. 145, 197–216...
    • 16. Ablowitz, M.J., Musslimani, M.J.: Integrable nonlocal nonlinear Schrödinger equation. Phys. Rev. Lett. 110, 064105 (2013)
    • 17. Fokas, A.S.: Integrable multidimensional versions of the nonlocal nonlinear Schrödinger equation. Nonlinearity 29, 319 (2016)
    • 18. Rao, J., Cheng, Y., He, J.: Rational and semirational solutions of the nonlocal Davey–Stewartson equations. Stud. Appl. Math. 139, 568–598...
    • 19. Zhou, Z.: Darboux transformations and global explicit solutions for nonlocal Davey–Stewartson I equation. Stud. Appl. Math. 141, 186–204...
    • 20. Peng, W., Tian, S., Zhang, T., Fang, Y.: Rational and semi-rational solutions of a nonlocal (2+1)- dimensional nonlinear Schrödinger...
    • 21. Liu, W., Li, L.: General soliton solutions to a (2+1)-dimensional nonlocal nonlinear Schrödinger equation with zero and nonzero boundary...
    • 22. Shi, C., Fu, H., Wu, C.: Soliton solutions to the reverse-time nonlocal Davey–Stewartson III equation. Wave Motion 104, 102744 (2021)
    • 23. Yang, B., Yang, J.: Transformations between nonlocal and local integrable equations. Stud. Appl. Math. 140, 178–201 (2018)
    • 24. Matveev, V.B., Salle, M.A.: Darboux Transformation and Solitons. Springer, Berlin (1991)
    • 25. Ablowitz, M.J., Clarkson, P.A.: Solitons. Nonlinear Evolution Equations and Inverse Scattering. Cambridge University Press, Cambridge...
    • 26. Ohta, Y., Yang, J.: Rogue waves in the Davey–Stewartson I equation. Phys. Rev. E 86(3), 036604 (2012)
    • 27. Ohta, Y., Wang, D., Yang, J.: General N-dark-dark solitons in the coupled nonlinear Schrödinger equations. Stud. Appl. Math. 127, 345–371...
    • 28. Ohta, Y., Yang, J.: Dynamics of rogue waves in the Davey–Stewartson II equation. J. Phys. A: Math. Theor. 46, 105202 (2013)
    • 29. Sheng, H.H., Yu, G.F.: Solitons, breathers and rational solutions for a (2 + 1)-dimensional dispersive long wave system. Physica D...
    • 30. Mel’nikov, V.K.: A direct method for deriving a multi-soliton solution for the problem of interaction of waves on the x, y plane. Commum....
    • 31. Sun, B., Lian, Z.: Rogue waves in the multicomponent Mel’nikov system and multicomponent Schrödinger–Boussinesq system. Pramana-J Phys...
    • 32. Sun, B., Wazwaz, A.M.: Interaction of lumps and dark solitons in the Mel’nikov equation. Nonlinear Dyn. 92, 2049–2059 (2018)
    • 33. Hase, Y., Hirota, R., Ohta, Y., Satsuma, J.: Soliton solutions to the Mel’nikov equations. J. Phys. Soc. Jpn. 58, 2713–2720 (1989)
    • 34. Zhang, Y., Sun, Y., Xiang, W.: The rogue waves of the KP equation with self-consistent sources. Appl. Math. Comput. 263, 204–213 (2015)
    • 35. Deng, S.F., Chen, D.Y., Zhang, D.J.: The multisoliton solutions of the KP equation with self-consistent sources. J. Phys. Soc. Jpn. 72,...
    • 36. Chvartatskyi, O., Dimakis, A., Müller-Hoissen, F.: Self-consistent sources for integrable equations via deformations of binary Darboux...
    • 37. Yong, X., Li, X., Huang, Y., Ma, W., Liu, Y.: Rational solutions and lump solutions to the (3 + 1)- dimensional Mel’nikov equation....
    • 38. Cao, Y., Tian, H., Wazwaz, A., Liu, J., Zhang, Z.: Interaction of wave structure in the PT-symmetric (3+1)-dimensional nonlocal Mel’nikov...
    • 39. Rao, J., He, J., Mihalache, D., Cheng, Y.: Dynamics of lump-soliton solutions to the PT-symmetric nonlocal Fokas system. Wave Motion 101,...
    • 40. Liu, Y., Li, B.: Dynamics of solitons and breathers on a periodic waves background in the nonlocal Mel’nikov equation. Nonlinear Dyn....
    • 41. Liu, W., Zheng, X., Li, X.: Bright and dark soliton solutions to the partial reverse space-time nonlocal Mel’nikov equation. Nonlinear...
    • 42. Hirota, R.: The Direct Method in Soliton Theory. Cambridge University Press, Cambridge (2004)
    • 43. Jimbo, M., Miwa, T.: Solitons and infinite-dimensional Lie algebras. Publ. Res. Inst. Math. Sci. 19, 943–1001 (1983)
    • 44. Fu, H., Lu, W., Guo, J., Wu, C.: General soliton and (semi-)rational solutions of the partial reverse space y-non-local Mel’nikov equation...
    • 45. Lin, Z., Wen, X.: Hodograph transformation, various exact solutions and dynamical analysis for the complex Wadati–Konno–Ichikawa-II equation....
    • 46. Liu, X., Wen, X.: A discrete KdV equation hierarchy: continuous limit, diverse exact solutions and their asymptotic state analysis. Commun....
    • 47. Liu, X., Wen, X., Zhang, T.: Magnetic soliton and breather interactions for the higher-order Heisenberg ferromagnetic equation via the...
    • 48. Liu, X., Wen, X.: Diverse soliton solutions and dynamical analysis of the discrete coupled mKdV equation with 4 × 4 Lax pair. Chin. Phys....
Fundación Dialnet

Mi Documat

Opciones de artículo

Opciones de compartir

Opciones de entorno