Solitons, Breathers and Modulation Instability for a Higher-Order Coupled Nonlinear Schrödinger System for the Ultrashort Optical Pulses in a Nonlinear Medium

• Dan-Yu Yang ^[1] ; Bo Tian ^[1] ; Yuan Shen ^[1] ; Xiao-Tian Gao ^[1]
  1. [1] Beijing University of Posts and Telecommunications

     Beijing University of Posts and Telecommunications

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 22, Nº 2, 2023
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • In this paper, we investigate some soliton and breather solutions for a higher-order coupled nonlinear Schrödinger system which may describe the ultrashort optical pulses in a nonlinear medium. With the help of the existing Darboux transformation, we construct the first- and second-order soliton solutions, as well as the first- and secondorder breather solutions. We present two types of the solitons, i.e., two-hump solitons and one-hump solitons. Interaction between the two one-hump solitons, and interaction between a two-hump soliton and a one-hump soliton are presented.When the velocities of two solitons are equal, we obtain the bound state of the two solitons. Real constant ε in the system affects the velocities of the solitons. We show the one breather and interaction between the two breathers. Velocities and shapes of the breathers are also affected by ε. We discuss the modulation instability of that system through the linear stability analysis. That system may describe the ultrashort optical pulses in a nonlinear medium, therefore the wave phenomena proposed in our paper may provide certain theoretical references for the related experiments in the future.

• Referencias bibliográficas
  • 1. Kundu, N., Ghosh, S., Roy, U.: Quantum simulation of rogue waves in Bose-Einstein condensate: an exact analytical method. Phys. Lett. A...
  • 2. Baals, C., Moreno, A.G., Jiang, J., Benary, J., Ott, H.: Stability analysis and attractor dynamics of three-dimensional dark solitons with...
  • 3. Kruglov, V.I., Triki, H.: Periodic and solitary waves in an inhomogeneous optical waveguide with third-order dispersion and self-steepening...
  • 4. Kippenberg, T.J., Gaeta, A.L., Lipson, M., Gorodetsky, M.L.: Dissipative Kerr solitons in optical microresonators. Science 361, 6402 (2018)
  • 5. Peregrine, D.H.: Water waves, nonlinear Schrödinger equations and their solutions. J. Aust. Math. Soc. Ser. B 25, 16 (1983)
  • 6. Henderson, K.L., Peregrine, D.H., Dold, J.W.: Unsteady water wave modulations: fully nonlinear solutions and comparison with the nonlinear...
  • 7. Kharif, C., Pelinovsky, E., Slunyaev, A.: Rogue Waves in the Ocean. Springer, Berlin (2009)
  • 8. Shrira, V.I., Geogjaev, V.V.: What makes the Peregrine soliton so special as a prototype of freak waves? J. Eng. Math. 67, 11 (2010)
  • 9. Baronio, F., Conforti, M., Degasperis, A., Lombardo, S., Onorato, M., Wabnitz, S.: Vector rogue waves and baseband modulation instability...
  • 10. Kanna, T., Sakkaravarthi, K.: Multicomponent coherently coupled and incoherently coupled solitons and their collisions. J. Phys. A 44,...
  • 11. Sakkaravarthi, K., Kanna, T.: Bright solitons in coherently coupled nonlinear Schrödinger equations with alternate signs of nonlinearities....
  • 12. Park, Q.H., Shin, H.J.: Painlevé analysis of the coupled nonlinear Schrödinger equation for polarized optical waves in an isotropic medium....
  • 13. Malomed, B.A.: Bound solitons in coupled nonlinear Schrödinger equations. Phys. Rev. A 45, R8321 (1992)
  • 14. Xu, T., Chen, Y., Lin, J.: Localized waves of the coupled cubic-quintic nonlinear Schrödinger equations in nonlinear optics. Chin. Phys....
  • 15. Du, Z., Tian, B., Qu, Q.X., Wu, X.Y., Zhao, X.H.: Vector rational and semi-rational rogue waves for the coupled cubic-quintic nonlinear...
  • 16. Sun, W.R., Liu, D.Y., Xie, X.Y.: Vector semirational rogue waves and modulation instability for the coupled higher-order nonlinear Schrödinger...
  • 17. Lan, Z.Z.: Rogue wave solutions for a coupled nonlinear Schrödinger equation in the birefringent optical fiber. Appl. Math. Lett. 98,...
  • 18. Du, Z., Ma, Y.P.: Beak-shaped rogue waves for a higher-order coupled nonlinear Schrödinger system with 4 × 4 Lax pair Appl. Math. Lett....
  • 19. Williams, J., Walser, R., Cooper, J., Cornell, E., Holland, M.: Nonlinear Josephson-type oscillations of a driven, two-component Bose-Einstein...
  • 20. Zhao, L.C., Ling, L.M., Yang, Z.Y., Liu, J.: Pair-tunneling induced localized waves in a vector nonlinear Schrödinger equation. Commun....
  • 21. Williams, J., Walser, R., Cooper, J., Cornell, E.A., Holland, M.: Excitation of a dipole topological state in a strongly coupled two-component...
  • 22. Ling, L.M., Zhao, L.C.: Integrable pair-transition-coupled nonlinear Schrödinger equations. Phys. Rev. E 92, 022924 (2015)
  • 23. Liu, C., Chen, S.C., Yao, X., Akhmediev, N.: Non-degenerate multi-rogue waves and easy ways of their excitation. Physica D 433, 133192...
  • 24. Chen, S.C., Liu, C.: Hidden Akhmediev breathers and vector modulation instability in the defocusing regime. Physica D 438, 133364 (2022)
  • 25. Che, W.J., Chen, S.C., Liu, C., Zhao, L.C., Akhmediev, N.: Nondegenerate Kuznetsov-Ma solitons of Manakov equations and their physical...
  • 26. Liu, C., Chen, S.C., Yao, X.K., Akhmediev, N.: Modulation instability and non-degenerate Akhmediev breathers of Manakov equations. Chin....
  • 27. Liu, D.Y., Sun, W.R.: Rational solutions for the nonlocal sixth-order nonlinear Schrödinger equation. Appl. Math. Lett. 84, 63 (2018)
  • 28. Xiang, X.S., Zuo, D.W.: Breather and rogue wave solutions of coupled derivative nonlinear Schrödinger equations. Nonlinear Dyn. 107, 1195...
  • 29. Liu, F.Y., Gao, Y.T.: Lie group analysis for a higher-order Boussinesq-Burgers system. Appl. Math. Lett. 132, 108094 (2022)
  • 30. Jia, H.X., Zuo, D.W., Tian, X.S., Guo, Z.F.: Characteristics of coexisting rogue wave and breather in vector nonlinear Schrödinger system....
  • 31. Gao, X.T., Tian, B., Shen, Y., Feng, C.H.: Considering the shallow water of a wide channel or an open sea through a generalized (2+1)-dimensional...
  • 32. Gao, X.T., Tian, B., Feng, C.H.: In oceanography, acoustics and hydrodynamics: investigations on an extended coupled (2+1)-dimensional...
  • 33. Gao, X.Y., Guo, Y.J., Shan,W.R.: Oceanic shallow-water symbolic computation on a (2+1)-dimensional generalized dispersive long-wave...
  • 34. Wang, M., Tian, B., Zhou, T.Y.: Darboux transformation, generalized Darboux transformation and vector breathers for a matrix Lakshmanan-Porsezian-Daniel...
  • 35. Yang, D.Y., Tian, B., Tian, H.Y., Wei, C.C., Shan, W.R., Jiang, Y.: Darboux transformation, localized waves and conservation laws for...
  • 36. Wu, X.H., Gao, Y.T., Yu, X., Liu, L.Q., Ding, C.C.: Vector breathers, rogue and breather-rogue waves for a coupled mixed derivative nonlinear...
  • 37. Shen, Y., B., Tian, Zhou, T.Y., Gao, X.T.: Shallow-water-wave studies on a (2+1)-dimensional HirotaSatsuma-Ito system: X-type soliton,...
  • 38. Gao, X.Y., Guo, Y.J., Shan, W.R.: Letter to the Editor on a (2+1)-dimensional variable-coefficient Sawada-Kotera system in plasma...
  • 39. Liu, F.Y., Gao, Y.T., Yu, X.: Rogue-wave, rational and semi-rational solutions for a generalized (3+1)- dimensional Yu-Toda-Sasa-Fukayama...
  • 40. Shen, Y., Tian, B., Zhou, T.Y., Gao, X.T.: N-fold Darboux transformation and solitonic interactions for the Kraenkel-Manna-Merle system...
  • 41. Gao, X.Y., Guo, Y.J., Shan, W.R.: On a Whitham-Broer-Kaup-like system arising in the oceanic shallow water. Chin. J. Phys. (2023).
  • 42. Wu, X.H., Gao, Y.T., Yu, X., Ding, C.C., Hu, L., Li, L.Q.: Binary Darboux transformation, solitons, periodic waves and modulation instability...
  • 43. Wu, X.H., Gao, Y.T., Yu, X., Ding, C.C., Li, L.Q.: Modified generalized Darboux transformation and solitons for a Lakshmanan-Porsezian-Daniel...
  • 44. Wu, X.H., Gao, Y.T., Yu, X., Ding, C.C.: N-fold generalized Darboux transformation and soliton interactions for a three-wave resonant...
  • 45. Gao, X.Y., Guo, Y.J., Shan, W.R.: Reflecting upon some electromagnetic waves in a ferromagnetic film via a variable-coefficient modified...
  • 46. Shen, Y., Tian, B.: Bilinear auto-Bäcklund transformations and soliton solutions of a (3+1)-dimensional generalized nonlinear evolution...
  • 47. Liu, D.Y., Yu, H.M.: Mixed localized wave solutions of the Hirota equation. Appl. Math. Lett. 118, 107154 (2021)
  • 48. Gao, X.Y., Guo, Y.J., Shan, W.R.: Regarding the shallow water in an ocean via a Whitham-BroerKaup-like system: hetero-Bäcklund transformations,...
  • 49. Shen, Y., B., Tian, Zhou, T.Y., Gao, X.T.: Nonlinear differential-difference hierarchy relevant to the Ablowitz-Ladik equation: Lax pair,...
  • 50. Gao, X.T., Tian, B.: Water-wave studies on a (2+1)-dimensional generalized variable-coefficient BoitiLeon-Pempinelli system. Appl....
  • 51. Zhou, T.Y., Tian, B.: Auto-Bäcklund transformations, Lax pair, bilinear forms and bright solitons for an extended (3+1)-dimensional...
  • 52. Zhou, T.Y., Tian, B., Y.Q., Chen, Y., Shen: Painlevé analysis, auto-Bäcklund transformation and analytic solutions of a (2+1)-dimensional...
  • 53. Shen, Y., Tian, B., Liu, S.H., Zhou, T.Y.: Studies on certain bilinear form, N-soliton, higher-order breather, periodic-wave and hybrid...
  • 54. Liu, F.Y., Gao, Y.T., Yu, X., Ding, C.C.: Wronskian, Gramian, Pfaffian and periodic-wave solutions for a (3+1)-dimensional generalized...
  • 55. Gao, X.Y., Guo, Y.J., Shan, W.R.: Symbolically computing the shallow water via a (2+1)-dimensional generalized modified dispersive...
  • 56. Zhou, T.Y., Tian, B., Zhang, C.R., Liu, S.H.: Auto-Bäcklund transformations, bilinear forms, multiple-soliton, quasi-soliton and hybrid...
  • 57. Gao, X.Y., Guo, Y.J., Shan, W.R., Du, Z., Chen, Y.Q.: Magnetooptic studies on a ferromagnetic material via an extended (3+1)-dimensional...
  • 58. Gao, X.Y., Guo, Y.J., Shan, W.R.: Bilinear auto-Bäcklund transformations and similarity reductions for a (3+1)-dimensional generalized...
  • 59. Wu, X.H., Gao, Y.T., Yu, X., Ding, C.C., Liu, F.Y., Jia, T.T.: Darboux transformation, bright and darkCbright solitons of an N-coupled...
  • 60. Nasreen, N., Seadawy, A.R., Lu, D., Arshad, M.: Construction of modulation instability analysis and optical soliton solutions of pertubed...
  • 61. Nasreen, N., Lu, D., Arshad, M.: Optical soliton solutions of nonlinear Schrödinger equation with second order spatiotemporal dispersion...
  • 62. Nasreen, N., Seadawy, A.R., Lu, D.: Study of modulation instability analysis and optical soliton solutions of higher-order dispersive...
  • 63. Seadawy, A.R., Lu, D., Nasreen, N., Nasreen, S.: Structure of optical solitons of resonant Schrödinger equation with quadratic cubic nonlinearity...
  • 64. Nasreen, N., Seadawy, A.R., Lu, D., Albarakati, W.A.: Dispersive solitary wave and soliton solutions of the gernalized third order nonlinear...
  • 65. Houwe, A., Saliou, Y., Djorwe, P., Abbagari, S., Akinyemi, L., Doka, S.Y.: Modulation instability gain and modulated wave shape incited...
  • 66. Csavina, J., Field, J., Félix, O., Corral-Avitia, A.Y., Sáez, A.E., Betterton, E.A.: Effect of wind speed and relative humidity on atmospheric...
  • 67. Abbagari, S., Houwe, A., Rezazadeh, H., Bekir, A., Bouetou, T.B., Crépin, K.T.: Reply on the comment on optical soliton to multi-core...
  • 68. Alphonse, H., Djorwe, P., Abbagari, S., Doka, S.Y., Engo, S.N.: Discrete solitons in nonlinear optomechanical array. Chaos Solitons Fract....
  • 69. Zakharov, V.E., Ostrovsky, L.A.: Modulation instability: the beginning. Physica D 238, 540 (2009)
  • 70. Ostrovskaya, E.A., Kivshar, Y.S., Skryabin, D.V., Firth, W.J.: Stability of multihump optical solitons. Phys. Rev. Lett. 83, 296 (1999)
  • 71. Pelinovsky, D.E., Yang, J.K.: Instabilities of multihump vector solitons in coupled nonlinear Schrödinger equations. Stud. Appl. Math....
  • 72. Porsezian, K., Kuriakose, V.C.: Optical Solitons: Theoretical and Experimental Challenges. Springer, New York (2003)
  • 73. Liu, C.,Wu, Y.H., Chen, S.C., Yao, X., Akhmediev, N.: Exact analytic spectra of asymmetric modulation instability in systems with self-steepening...
  • 74. Chen, S.C., Liu, C., Yao, X., Zhao, L.C., Akhmediev, N.: Extreme spectral asymmetry of Akhmediev breathers and Fermi-Pasta-Ulam recurrence...