Mixed Higher-Order Rogue Waves and Solitons for the Coupled Modified Nonlinear Schrödinger Equation

• Tao Xu ^[1] ; Guoliang He ^[1] ; Ming Wang ^[1] ; Yanqing Wang ^[1]
  1. [1] Zhengzhou University of Light Industry

     Zhengzhou University of Light Industry

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 22, Nº 1, 2023
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • The coupled modified nonlinear Schrödinger equation, which appears in birefringent optical fibers and describes the propagation of the short pluses in picosecond or femtosecond regions, is researched by the Darboux transformation. Utilizing both the Darboux transformation and the received special vector solution of the Lax pair, the general solutions for the coupled modified nonlinear Schrödinger equation are generated. Through searching the double-root condition of the spectral characteristic equation for the matrix in the Lax pair, we can obtain the reduced solutions that mixed higher-order rogue waves and solitons. Besides, the reduced solutions are mainly discussed in the following two types: (1) one component includes higher-order rogue waves and multi-bright-solitons, the other one is higher-order rogue waves and multidark-solitons; (2) higher-order rogue waves as the degenerate case. The dynamical behaviors of these reduced solutions are detailedly discussed.

• Referencias bibliográficas
  • 1. Chen, S.H., Baronio, F., Soto-Crespo, J.M., Grelu, P., Mihalache, D.: Versatile rogue waves in scalar, vector, and multidimensional nonlinear...
  • 2. Li, R.M., Geng, X.G.: On a vector long wave-short wave-type model. Stud. Appl. Math. 144, 1–21 (2019)
  • 3. Zhang, G.Q., Ling, L.M., Yan, Z.Y.: Multi-component nonlinear Schrödinger equations with nonzero boundary conditions: higher-order vector...
  • 4. Akhmediev, N.: Waves that appear from nowhere: complex rogue wave structures and their elementary particles. Front. Phys. 8, 612318 (2021)
  • 5. Mihalache, D.: Localized structures in optical and matter-wave media: a selection of recent studies. Rom. Rep. Phys. 73, 403 (2021)
  • 6. Ling, L.M., Guo, B.L., Zhao, L.C.: High-order rogue waves in vector nonlinear Schrödinger equations. Phys. Rev. E 89, 041201(R) (2014)
  • 7. Weng, W.F., Zhang, G.Q., Wang, L., Zhang, M.H., Yan, Z.Y.: Rational vector rogue waves for the n-component Hirota equation with non-zero...
  • 8. Li, B.Q., Ma, Y.L.: Interaction properties between rogue wave and breathers to the manakov system arising from stationary self-focusing...
  • 9. Li, B.Q., Ma, Y.L.: A ‘firewall’ effect during the rogue wave and breather interactions to the Manakov system. Nonlinear Dyn. (2022). https://doi.org/10.1007/s11071-022-07878-6
  • 10. Guan, W.Y., Li, B.Q.: Asymmetrical and self-similar structures of optical breathers for the Manakov system in photorefractive crystals...
  • 11. Sinthuja, N., Manikandan, K., Senthilvelan, M.: Formation of rogue waves on the periodic background in a fifth-order nonlinear Schrödinger...
  • 12. Manikandan, K., Vishnu Priya, N., Senthilvelan, M., Sankaranarayanan, R.: Higher-order matter rogue waves and their deformations in two-component...
  • 13. Sinthuja, N., Manikandan, K., Senthilvelan, M.: Rogue waves on an elliptic function background in complex modified Korteweg-de Vries equation....
  • 14. Sinthuja, N., Manikandan, K., Senthilvelana, M.: Rogue waves on the double-periodic background in Hirota equation. Eur. Phys. J. Plus...
  • 15. Manikandan, K., Senthilvelan, M.: An analysis of spatiotemporal localized solutions in the variable coefficients (3+1)-dimensional...
  • 16. Li, B.Q., Ma, Y.L.: Extended generalized Darboux transformation to hybrid rogue wave and breather solutions for a nonlinear Schrödinger...
  • 17. Li, B.Q., Ma, Y.L.: Interaction dynamics of hybrid solitons and breathers for extended generalization of Vakhnenko equation. Nonlinear...
  • 18. Li, B.Q.: Hybrid breather and rogue wave solution for a (2 + 1)-dimensional ferromagnetic spin chain system with variable coefficients....
  • 19. Ma, Y.L., Li, B.Q.: Hybrid rogue wave and breather solutions for a complex mKdV equation in fewcycle ultra-short pulse optics. Eur. Phys....
  • 20. Ma, Y.L., Wazwaz, A.M., Li, B.Q.: New extended Kadomtsev-Petviashvili equation: multiple soliton solutions, breather, lump and interaction...
  • 21. Feng, B.F.: General N-soliton solution to a vector nonlinear Schrödinger equation. J. Phys. A: Math. Theor. 47, 355203 (2014)
  • 22. Chen, J.C., Chen, Y., Feng, B.F., Maruno, K.: General mixed multi-soliton solutions to one-dimensional multi-component Yajima-Oikawa system....
  • 23. Han, Z., Chen, Y., Chen, J.C.: Bright-dark mixed N-soliton solutions of the multi-component Mel’nikov system. J. Phys. Soc. Jpn. 86, 104008...
  • 24. Baronio, F., Degasperis, A., Conforti, M., Wabnitz, S.: Solutions of the vector nonlinear Schrödinger equations: evidence for deterministic...
  • 25. Ling, L.M., Zhao, L.C.: Modulational instability and homoclinic orbit solutions in vector nonlinear Schrödinger equation. Commun. Nonlinear...
  • 26. Zhang, G.Q., Yan, Z.Y.: Three-component nonlinear Schrödinger equations: modulational instability, Nth-order vector rational and semi-rational...
  • 27. Rao, J.G., Porsezian, K., He, J.S., Kanna, T.: Dynamics of lumps and dark-dark solitons in the multicomponent long-wave-short-wave resonance...
  • 28. Zhao, L.C., Liu, J.: Localized nonlinear waves in a two-mode nonlinear fiber. J. Opt. Soc. Amer. B 29, 3119C3127 (2012)
  • 29. Lin, S.N., Chen, Y.: A two-stage physics-informed neural network method based on conserved quantities and applications in localized wave...
  • 30. Xu, T., Chen, Y.: Mixed interactions of localized waves in the three-component coupled derivative nonlinear Schrödinger equations. Nonlinear...
  • 31. Chen, S.H.: Twisted rogue-wave pairs in the Sasa-Satsuma equation. Phys. Rev. E 88, 023202 (2013)
  • 32. Ye, Y.L., Zhou, Y., Chen, S.H., Baronio, F., Grelu, P.: General rogue wave solutions of the coupled Fokas-Lenells equations and non-recursive...
  • 33. Xu, T., Chan, W.H., Chen, Y.: Higher-order rogue wave pairs in the coupled cubic-quintic nonlinear Schrödinger equations. Commun. Theor....
  • 34. Zhao, L.C., Liu, J.: Rogue-wave solutions of a three-component coupled nonlinear Schrödinger equation. Phys. Rev. E 87, 013201 (2013)
  • 35. Chen, J.B., Pelinovsky, D.E.: Periodic travelling waves of the modified KdV equation and rogue waves on the periodic background. J. Nonlinear...
  • 36. Feng, B.F., Ling, L.M., Takahashi, D.A.: Multi-breather and high-order rogue waves for the nonlinear Schrödinger equation on the elliptic...
  • 37. Mu, G., Qin, Z.Y., Grimshaw, R.: Dynamics of rogue waves on a multi-soliton background in a vector nonlinear Schrödinger equation. SIAM...
  • 38. Hisakado, M., Iizuka, T., Wadati, M.: Coupled hybrid nonlinear Schrödinger equation and optical solitons. J. Phys. Soc. Jpn. 63, 2887...
  • 39. Hisakado, M., Wadati, M.: Integrable multi-componet hybrid nonlinear Schrödinger equations. J. Phys. Soc. Jpn. 64, 408 (1995)
  • 40. Zhang, H.Q., Tian, B., Lü, X., Li, H., Meng, X.H.: Soliton interaction in the coupled mixed derivative nonlinear Schrödinger equations....
  • 41. Zhang, H.Q.: Darboux transformation and N-soliton solution for the coupled modified nonlinear Schrödinger equations. Z. Naturf. A 67,...
  • 42. Li, M., Tian, B., Liu, W.J., Jiang, Y., Sun, K.: Dark and anti-dark vector solitons of the coupled modified nonlinear Schrödinger equations...
  • 43. Wadati, M., Konno, K., Ichikawa, Y.H.: A generalization of inverse scattering method. J. Phys. Soc. Jpn. 46, 1965–1966 (1979)
  • 44. He, J.S., Xu, S.W., Cheng, Y.: The rational solutions of the mixed nonlinear Schrödinger equation. AIP Adv. 5, 017105 (2015)
  • 45. W. B. Li, C. Y. Xue, L. L. Sun, The general mixed nonlinear Schrödinger equation: darboux transformation, rogue wave solutions, and modulation...
  • 46. Wu, Q.L., Zhang, H.Q.: Breathers, rogue waves and breather-rogue waves on a periodic background for the modified nonlinear Schrödinger...
  • 47. Chowdhury, A.R., Paul, S., Sen, S.: Periodic solutions of the mixed nonlinear Schrödinger equation. Phys. Rev. D 32, 12 (1985)
  • 48. Matsuno, Y.: The N-soliton solution of a two-component modified nonlinear Schrödinger equation. Phys. Lett. A 375, 3090–3094 (2011)
  • 49. Janutka, A.: Collisions of optical ultra-short vector pulses. J. Phys. A: Math. Theor. 41, 285204 (2008)
  • 50. Hisakado, M., Wadati, M.: Integrable multi-component hybrid nonlinear Schrödinger equations. J. Phys. Soc. Japan 64, 408–413 (1995)
  • 51. Matsuno, Y.: The bright N-soliton solution of a multi-component modified nonlinear Schrödinger equation. J. Phys. A: Math. Theor. 44,...
  • 52. Matsuno, Y.: The multi-component modified nonlinear Schrödinger system with nonzero boundary conditions. Phys. Scr. 94, 115216 (2019)
  • 53. Yan, X.W.: Lax pair, Darboux-dressing transformation and localized waves of the coupled mixed derivative nonlinear Schrödinger equation...
  • 54. Xu, T., He, G.L.: The coupled derivative nonlinear Schrödinger equation: conservation laws, modulation instability and semirational solutions....
  • 55. Baronio, F., Conforti, M., Degasperis, A., Lombardo, S., Onorato, M., Wabnitz, S.: Vector rogue waves and baseband modulation instability...
  • 56. Baronio, F., Chen, S., Grelu, P., Wabnitz, S., Conforti, M.: Baseband modulation instability as the origin of rogue waves. Phys. Rev....
  • 57. Guo, B.L., Ling, L.M., Liu, Q.P.: Nonlinear Schrödinger equation: generalized Darboux transformation and rogue wave solutions. Phys. Rev....