Multiple Soliton Asymptotics in a Nonlinear Optical Fiber

• Hong-Wen Shan ^[1] ; Bo Tian ^[1] ; Xiao-Tian Gao ^[1] ; Hao-Dong Liu ^[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. 24, Nº 6, 2025
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • Nonlinear optical fibers are supposed as one of the effective transmission media which can be applied in the optical fiber communication. A Lax-integrable (2+1)-dimensional Kundu-Mukherjee-Naskar equation, which describes the propagation of optical pulses in a nonlinear optical fiber, is investigated in this paper. We first construct the N-fold binary Darboux transformation, where N is a positive integer. Via the obtained Nfold binary Darboux transformation, we derive the N-soliton solutions and perform the asymptotic analysis on the obtained N-soliton solutions. The N-soliton solutions can be decomposed into N one-soliton solutions with different velocities as y → ±∞, where y is a spatial variable. Before and after each interaction, the N solitons pass through each other without any change in shape, velocity, while only encounter the phase shifts. Taking N = 2 and N = 3 as two examples, we graphically illustrate the 2 and 3 interacting solitons through the 3D plots and density plots, which align with our asymptotic-analysis results. Our results might help people understand some localized waves in nonlinear optical fibers.

• Referencias bibliográficas
  • 1. Fan, W., Liang, Y., Han, T.: Novel insights into high-order dispersion and soliton dynamics in optical fibers via the perturbed Schrödinger-Hirota...
  • 2. Das, P.K.: Three interaction scenarios of two orthogonally polarised optical pulses modelled by the variable coefficient coupled nonlinear...
  • 3. Oxenløwe, L.K.: Optical frequency combs for optical fiber communications. APL Photonics 10, 010901 (2025)
  • 4. Liu, Z., Liu, T.G., Zhao, J., Uduagbomen, J., Wang, Y.L., Popov, S.: A module to enhance the generalization ability of end-to-end deep...
  • 5. Hontinfinde, R.D., Ayela, M.A., Edah, G.: Dynamics of optical soliton solutions parameters for Hirota equation by variational principle....
  • 6. Rehman, S.U., Bilal, M., Ren, J.L., Bayram, M., Inc, M.: Sensitivity analysis and dynamics of optical dromions in conformable generalized...
  • 7. Liu, H.Y., Liu, L., Zhang, P.Q., Dai, S.X., Wu, D.D.: A nonlinear fiber resonator-based optical soliton information encoder. Opt. Laser...
  • 8. Bashar, M.H., Mannaf, M.A., Rahman, M.M., Khatun, M.T.: Optical soliton solutions of the Mfractional paraxial wave equation. Sci. Rep....
  • 9. Gaballah, M., El-Shiekh, R.M.: Novel picosecond wave solutions and soliton control for a higher-order nonlinear Schrödinger equation with...
  • 10. Muhammad, A.S.M.: Soliton solutions of cubic quintic septimal nonlinear Schrödinger wave equation with conformable derivative by two distinct...
  • 11. Gu, Y.Y., Zhang, X.T., Huang, Z.S., Peng, L.D., Lai, Y.K., Aminakbari, N.: Soliton and lump and travelling wave solutions of the (3+1)...
  • 12. Saber, H., Alqarni, F.A., Aldwoah, K.A., Hashim, H.E., Saifullah, S., Hleili, M.: Novel hybrid waves solutions of Sawada-Kotera like integrable...
  • 13. Liu, J.G.: Soliton structures for the (3+1)-dimensional Painlevé integrable equation in fluid mediums. Sci. Rep. 14, 11581 (2024)
  • 14. Wang, Y., Zhao, Z., Xin, P.: Numerical calculation and characteristics of N-periodic waves of a (4+1)- dimensional Korteweg-de Vries-Calogero-Bogoyavlenskii-Schiff...
  • 15. Shakeel, K., Lupas, A.A., Abbas, M., Mohammed, P.O., Abdullah, F.A., Abdelwahed, M.: Construction of soliton solutions of time-fractional...
  • 16. Wang, S.N., Sheng, H.H., Yu, G.F.: Dynamics of the coupled (2+1)-dimensional Fokas system. Z. Angew. Math. Phys. 76, 32 (2025)
  • 17. Gao, X.Y., Zhao, W.G., Zuo, D.W.: Bilinear forms, bilinear auto-Bäcklund transformations and similarity reductions for a (3+1)-dimensional...
  • 18. Wang, G.W., Tan, Z.X., Gao, X.Y., Liu, J.G.: A new (2+1)-dimensional like-Harry-Dym equation with derivation and soliton solutions....
  • 19. Yang, D.Y.: Degenerate soliton solutions and their dynamics in a coupled generalized nonlinear Schrödinger equations with the four-wave...
  • 20. Gao, X.Y., Liu, J.G., Wang, G.W.: Inhomogeneity, magnetic auto-Bäcklund transformations and magnetic solitons for a generalized variable-coefficient...
  • 21. Gao, X.Y.: Hetero-Bäcklund transformation, bilinear forms and multi-solitons for a (2+1)-dimensional generalized modified dispersive...
  • 22. Mandal, S., Sil, S., Ghosh, S.: On the Lie symmetry analysis of three-dimensional perturbed shear flows. Chaos, Soliton Fract. 191, 115875...
  • 23. Chen, S.S.: Multi-geometric discrete spectral problem with several pairs of zeros for Sasa-Satsuma equation. Appl. Math. Lett. 160, 109307...
  • 24. Chen, S.S., Tian, B., Tian, H.Y., Hu, C.C.: Riemann-Hilbert approach, dark solitons and double-pole solutions for Lakshmanan-Porsezian-Daniel...
  • 25. Dong, Y.K., Sadiq, K., Scherzer, O., Schotland, J.C.: Computational inverse scattering with internal sources: A reproducing Kernel Hilbert...
  • 26. Vinayagam, P.S., Radha, R.: Robust dynamics of rogue waves, breathers and mixed bound state solutions in spin-orbit and Rabi coupled condensates....
  • 27. Riaz, H.W.A., Lin, J., Wang, J.: On an extended semi-discrete matrix coupled dispersionless system: Darboux transformation and explicit...
  • 28. Ma, W.X.: Soliton solutions to Sasa-Satsuma-Type modified Korteweg-de Vries equations by binary Darboux transformations. Mathematics 12,...
  • 29. Inam, A., ul Hassan, M.: Quasi-Grammian soliton and kink dynamics of an M-component semidiscrete coupled integrable system. Theor. Math....
  • 30. Song, C., Zhao, H.Q., Zhu, Z.N.: Nonlocal Yajima-Oikawa system: binary Darboux transformation, exact solutions and dynamic properties....
  • 31. Khater,M.M.A.: Novel computational simulation of the propagation of pulses in optical fibers regarding the dispersion effect. Int. J....
  • 32. Yusuf, A., Sulaiman, T.A., Mirzazadeh, M., Hosseini, K.: M-truncated optical solitons to a nonlinear Schrödinger equation describing the...
  • 33. Fermann, M.E., Kruglov, V., Thomsen, B., Dudley, J.M., Harvey, J.D.: Self-similar propagation and amplification of parabolic pulses in...
  • 34. Mollenauer, L.F., Stolen, R.H., Gordon, J.P.: Experimental observation of picosecond pulse narrowing and solitons in optical fibers. Phys....
  • 35. Wu, X.H., Gao, Y.T.: N-soliton asymptotic analysis on the Gerdjikov-Ivanov equation for the Alfvén waves in a plasma. Appl. Math. Lett....
  • 36. Wu, X.H., Gao, Y.T., Yu, X.: Dark-soliton asymptotics for a repulsive nonlinear system in a baroclinic flow. Phys. Fluids 36, 056615 (2024)
  • 37. Wu, X.H., Gao, Y.T.: Certain (2+1)-dimensional multi-soliton asymptotics in the shallow water. Chaos Soliton Fract. 188, 115460 (2024)
  • 38. Yang, D.Y., Du, Z.: Asymptotic analysis of double-hump solitons for a coupled fourth-order nonlinear Schrödingier system in a birefringent...
  • 39. Kundu, A., Mukherjee, A., Naskar, T.: Modelling rogue waves through exact dynamical lump soliton controlled by ocean currents. Proc. R....
  • 40. Mukherjee, A.: Atypical shaped (2+1) dimensional solitons in optical nanofibers. Opt. Quant. Electron. 56, 669 (2024)
  • 41. Ghanbari, B., Baleanu, D.: Abundant optical solitons to the (2+1)-dimensional Kundu-MukherjeeNaskar equation in fiber communication...
  • 42. Aydemir, T.: Application of the generalized unified method to solve (2+1)-dimensional KunduMukherjee-Naskar equation. Opt. Quant....
  • 43. Tang, Y.: Applying a transformation-based method to extract optical traveling waves from the KunduMukherjee-Naskar equation. Results Phys....
  • 44. Cakicioglu, H., Cinar, M., Secer, A., Bayram, M.: Optical solitons for Kundu-Mukherjee-Naskar equation via enhanced modified extended...
  • 45. Wang, K.J., Si, J., Liu, J.H.: Diverse optical soliton solutions to the Kundu-Mukherjee-Naskar equation via two novel techniques. Optik...
  • 46. Yue, X.G., Kaplan, M., Kaabar, M.K.A., Yang, H.M.: Exploring new features for the (2+1)-dimensional Kundu-Mukherjee-Naskar equation...
  • 47. Zafar, A., Raheel, M., Ali, K.K., Inc, M., Qaisar, A.: Optical solitons to the Kundu-Mukherjee-Naskar equation in (2+1)-dimensional...
  • 48. Onder, I., Secer, A., Ozisik, M., Bayram, M.: On the optical soliton solutions of Kundu-MukherjeeNaskar equation via two different analytical...
  • 49. Ren, M.R., Zhou, Y.Q., Liu, Q.: Traveling wave solutions of the generalized (2+1)-dimensional KunduMukherjee-Naskar equation. J. Appl....
  • 50. Al-Ghafri, K.S.: Soliton structures in optical fiber communications with Kundu-Mukherjee-Naskar model. Open Phys. 19, 679 (2021)
  • 51. Bilal, M., Shafqat-Ur-Rehman, Ahmad, J.: Investigation of optical solitons and modulation instability analysis to the Kundu-Mukherjee-Naskar...
  • 52. Rezazadeh, H., Kurt, A., Tozar, A., Tasbozan, O., Mirhosseini-Alizamini, S.M.: Wave behaviors of Kundu-Mukherjee-Naskar model arising...
  • 53. Triki, H., Benlalli, A., Zhou, Q., Biswas, A., Yıldırım, Y., Alzahrani, A.k., Belic, M.R.: Gray optical dips of Kundu-Mukherjee-Naskar...
  • 54. Kumar, D., Paul, G.C., Biswas, T., Seadawy, A.R., Baowali, R., Kamal, M., Rezazadeh, H.: Optical solutions to the Kundu-Mukherjee-Naskar...
  • 55. Constantinescu, R., Florian, A.: Integrability via functional expansion for the KMN model. Symmetry 12, 1819 (2020)
  • 56. Shafqat-ur-Rehman, Ahmad, J.: Stability analysis and novel optical pulses to Kundu-MukherjeeNaskar model in birefringent fibers. Int....
  • 57. Ke, A., Li. J.B.: Exact solutions and dynamics of Kundu-Mukherjee-Naskar model. J. Appl. Anal. Comput. 14, 1014 (2024)
  • 58. Cimpoiasu, R., Rezazadeh, H., Florian, D.A., Ahmad, H., Nonlaopon, K., Altanji, M.: Symmetry reductions and invariant-group solutions...
  • 59. Zhao, D., Lao, Z.Q.: Riemann-Hilbert approach for a (2+1) dimensional Kundu-Mukherjee-Naskar equation. Nonlinear Dyn. 112, 12335 (2024)
  • 60. Wen, X.Y.: Higher-order rational solutions for the (2+1)-dimensional KMN equation. Proc. Rom. Acad. Ser. A Math. Phys. 18, 191 (2017)
  • 61. Qiu, D.Q., Zhang, Y.S., He, J.S.: The rogue wave solutions of a new (2+1)-dimensional equation. Commun. Nonlinear. Sci. Numer. Simulat....
  • 62. Wang, H.T., Wen, X.Y.: Modulational instability and mixed breather-lump interaction solutions in the (2+1)-dimensional KMN equation....
  • 63. Wu, X.H., Gao, Y.T.: Multi-breather asymptotics for a nonlinear Schrödinger equation arising in oceanography, plasma physics, Bose-Einstein...
  • 64. Ali, A., Kalisch, H.: On the formulation of mass, momentum and energy conservation in the KdV equation. Acta Appl. Math. 133, 113 (2014)