Discussion on Soliton Solutions and Bilinear Bäcklund Transformation of a Generalized Coupled Higher-Order Nonlinear Schrödinger System with Variable Coefficients

• Yating Hao ^[1] ; Ben Gao ^[1]
  1. [1] Taiyuan University of Technology

     Taiyuan University of Technology

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 4, 2025
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • What is studied in this article is a generalized coupled higher-order nonlinear Schrödinger system with variable coefficients, which reveals the technical challenges of transmitting two ultrashort pulses at the same time in the inhomogeneous fibers, and plays a particularly critical role in driving further development in the field of telecommunication. By utilizing the Hirota bilinear method, we derive the Hirota bilinear form of the above system and obtain bright-dark alternating one-, two-, threeand even N-soliton solutions step by step, achieving the expected goal. On this basis, the obtained soliton solutions were further studied to explore the physical meanings contained therein. After assigning some suitable values to the unknown parameters, different types of soliton solutions, such as wave type, U-type and so on, are analyzed and discussed graphically. It is also concluded that parameters α2(z), α3(z) and α6(z) jointly affect the overall trajectories of soliton solutions, while the selection of other parameters affects part of the trajectories during the movement. Furthermore, the dynamic behaviors of the two-soliton solutions before and after the collision are studied by means of asymptotic analysis. They are presented intuitively in the form of numerical values such as amplitude, velocity and initial phase. Ultimately, we further study the bilinear Bäcklund transformation of the above system and obtain new soliton solutions. The work done in this paper contributes to a deeper physical understanding of the above system, and provides certain theoretical guidance for further improvements in modern communication, such as increasing transmission capacity, enhancing signal stability and reducing energy consumption.

• Referencias bibliográficas
  • 1. Akyüz, C., Erman, F., Uncu, H.: The Harmonic Oscillator Potential Perturbed by a Combination of Linear and Non-linear Dirac Delta Interactions...
  • 2. Tang, Y.N., Liang, Z.J., Xie, W.X.: The local wave phenomenon in the quintic nonlinear Schrödinger equation by numerical methods. Nonlinear...
  • 3. Yang, L., Gao, B.: Solitons, kink-solitons and breather solutions of the two-coupled incoherent nonlinear Schrödinger equation. Nonlinear...
  • 4. Berrada, K., Sabik, A., Khalil, E.M., Abdel-Khalek, S.: Geometric phase and Wehrl phase entropy for two superconducting qubits in a coherent...
  • 5. Hashemi, M.S.: A variable coefficient third degree generalized Abel equation method for solving stochastic Schrödinger-Hirota model. Chaos,...
  • 6. Singh, A., Gupta, N.: Electron plasma wave excitation by beating of two q-Gaussian laser beams in collisionless plasma. Laser Part. Beams...
  • 7. Dey, A., Chandra, S., Das, C., Mandal, S., Das, T.: Rogue Wave Generation Through Nonlinear SelfInteraction of Electrostatic Waves in Dense...
  • 8. El-Tantawy, S.A., Alharbey, R.A., Salas, A.H.: Novel approximate analytical and numerical cylindrical rogue wave and breathers solutions:...
  • 9. Chen, L., Zhu, H.P.: Partially nonlocal bright-dark rogue waves and bright-bright rogue wave pairs of a vector nonlinear Schrödinger equation....
  • 10. Mathanaranjan, T., Hashemi, M.S., Rezazadeh, H., Akinyemi, L., Bekir, A.: Chirped optical solitons and stability analysis of the nonlinear...
  • 11. Chen, J.C., Yan, Q.X.: Bright soliton solutions to a nonlocal nonlinear Schrödinger equation of reversetime type. Nonlinear Dyn. 100(3),...
  • 12. Jia, H.Y., Abdalla,M.E.M., Idris, S.A., Rezapour, S., Shateyi, S., Alsallami, S.A.M.: On novel analytical solutions to a generalized Schrödinger’s...
  • 13. Younas, U., Sulaiman, T.A., Ren, J.L.: Dynamics of optical pulses in dual-core optical fibers modelled by decoupled nonlinear Schrödinger...
  • 14. Wang, M.L., Zhang, J.L., Li, L.X.: The decay mode solutions of the cylindrical/spherical nonlinear Schrödinger equation. Appl. Math. Lett....
  • 15. Bai, R.B., Wu, Y.F., Xue, J.: Optimal small data scattering for the generalized derivative nonlinear Schrödinger equations. J. Differential...
  • 16. Yang, L., Gao, B.: The nondegenerate solitons solutions for the generalized coupled higher-order nonlinear Schrödinger equations with...
  • 17. Wang, X.M., Hu, X.X.: Controllable vector soliton in (2+1)-dimensional coupled nonlinear Schrödinger equations with varying coefficients....
  • 18. Cui, H.G., Shan, W.R., Li, Q.Q., Cui, W.X.: High-order semi-rational solutions of the coupled nonlinear Schrödinger equations with variable...
  • 19. Wazwaz, A.M.: Optical bright and dark soliton solutions for coupled nonlinear Schrödinger (CNLS) equations by the variational iteration...
  • 20. Li, Z., Li, P., Han, T.Y.: Dynamical Behavior and the Classification of Single Traveling Wave Solutions for the Coupled Nonlinear Schrödinger...
  • 21. Shen, Y., Tian, B., Zhou, T.Y., Cheng, C.D.: Localized waves of the higher-order nonlinear SchrödingerMaxwell-Bloch system with the sextic...
  • 22. Shen, Y.: Dynamics of certain localized waves in an erbium-doped fiber system with the quintic terms. Chaos, Solitons & Fractals 192,...
  • 23. Younas, U., Sulaiman, T.A., Ren, J.L., Yusuf, A.: Lump interaction phenomena to the nonlinear illposed Boussinesq dynamical wave equation....
  • 24. Izgi, Z.P.: Rogue waves and solitons of the generalized modified nonlinear Schrödinger equations. Math. Comput. Simul. 208, 535–549 (2023)
  • 25. Barletti, L., Brugnano, L., Gurioli, G., Iavernaro, F.: Recent advances in the numerical solution of the Nonlinear Schrödinger Equation....
  • 26. Bai, Y.S., Liu, Y.N., Ma, W.X.: Lie symmetry analysis, exact solutions and conservation laws to multicomponent nonlinear Schrödinger equations....
  • 27. Tang, J.X.: Dynamical properties, chirped solutions, and chaotic behaviors of the extended nonlinear Schrödinger equation. Math. Methods...
  • 28. Xia, B.Q.: Vector nonlinear Schrödinger equation with an integrable defect and new integrable boundary conditions. Physica D 450, 133769...
  • 29. Lü, X., Li, J., Zhang, H.Q., Xu, T., Li, L.L., Tian, B.: Integrability aspects with optical solitons of a generalized variable-coefficient...
  • 30. Porsezian, K., Sundaram, P.S., Mahalingam, A.: Coupled higher-order nonlinear Schrödinger equations in nonlinear optics: Painlevé analysis...
  • 31. Arora, G., Rani, R., Emadifar, H.: Soliton: A dispersion-less solution with existence and its types. Heliyon 8(12), e12122 (2022)
  • 32. Mohan, B., Kumar, S., Kumar, R.: On investigation of kink-solitons and rogue waves to a new integrable (3+1)-dimensional KdV-type...
  • 33. Younas, U., Seadawy, A.R., Younis, M., Rizvi, S.T.R.: Construction of analytical wave solutions to the conformable fractional dynamical...
  • 34. Chen, J.C., Feng, B.F., Chen, Y., Ma, Z.Y.: General bright-dark soliton solution to (2+1)-dimensional multi-component long-wave-short-wave...
  • 35. Mohan, B., Kumar, S.: Painlevé analysis, restricted bright-dark N-solitons, and N-rogue waves of a (4+1)-dimensional variable-coefficient...
  • 36. Chen, L., Chen, J.C., Chen, Q.Y.: Mixed lump-soliton solutions to the two-dimensional Toda lattice equation via symbolic computation....
  • 37. Shen, Y.: An extended (3+1)-dimensional Bogoyavlensky-Konopelchenko equation: Pfaffian solutions and nonlinear wave interactions....
  • 38. Younas, U., Sulaiman, T.A., Ren, J.L.: On the optical soliton structures in the magneto electro-elastic circular rod modeled by nonlinear...
  • 39. Chen, J.C., Feng, B.F.: Tau-function formulation for bright, dark soliton and breather solutions to the massive Thirring model. Stud....
  • 40. Younas, U., Sulaiman, T.A., Ren, J.L.: Propagation of M-truncated optical pulses in nonlinear optics. Opt. Quant. Electron. 55(2), 102...
  • 41. Younas, U., Sulaiman, T.A., Ren, J.L.: Diversity of optical soliton structures in the spinor Bose-Einstein condensate modeled by three-component...
  • 42. Wang, Y.T., Li, C.X., Chen, F.L., Lan, H.W., Fu, S.N., Klimczak, M., Buczy ´nski, R., Tang, X.H., Tang, M., Zhao, L.M.: A prince for the...
  • 43. Kumar, S., Mohan, B., Kumar, R.: Lump, soliton, and interaction solutions to a generalized two-mode higher-order nonlinear evolution equation...
  • 44. Zhang, K., Han, T.Y.: The optical soliton solutions of nonlinear Schrödinger equation with quintic non-Kerr nonlinear term. Results in...
  • 45. Wei, J., Wang, J.Y., Li, Y.H.: Soliton and breather solutions of a reverse time nonlocal coupled nonlinear Schrödinger equation with four-wave...
  • 46. Liu, L., Tian, B., Chai, J., Chai, H.P.: Soliton interactions for a generalized variable-coefficient coupled higher-order nonlinear Schrödinger...
  • 47. Mou, D.S., Dai, C.Q.: Nondegenerate solitons and collision dynamics of the variable-coefficient coupled higher-order nonlinear Schrödinger...
  • 48. Gao, Z.Y., Song, S.N., Zhang, K., Guo, X.J.: The application of generalized coupled higher-order nonlinear Schrödinger equations with...
  • 49. Zhou, Q., Xu, M.Y., Sun, Y.Z., Zhong, Y., Mirzazadeh, M.: Generation and transformation of dark solitons, anti-dark solitons and dark...
  • 50. Yu, W.T., Luan, Z.T., Zhang, H.X., Liu, W.J.: Collisions of three higher order dark double- and singlehump solitons in optical fiber....
  • 51. Liu, L., Tian, B., Xie, X.Y., Guan, Y.Y.: Vector bright soliton behaviors of the coupled higher-orde nonlinear Schrödinger system in the...
  • 52. Sun, W.R., Tian, B., Wang, Y.F., Zhen, H.L.: Dark single- and double-hump vector solitons of the coupled higher-order nonlinear Schrödinger...
  • 53. Mohan, B., Kumar, S.: Rogue-wave structures for a generalized (3+1)-dimensional nonlinear wave equation in liquid with gas bubbles....
  • 54. Younas, U., Sulaiman, T.A., Ren, J.L.: On the collision phenomena to the (3+1)-dimensional generalized nonlinear evolution equation:...
  • 55. Chen, J.C., Yang, B., Feng, B.F.: Rogue waves in the massive Thirring model. Stud. Appl. Math. 151(3), 1020–1052 (2023)
  • 56. Shen, Y., Tian, B., Cheng, C.D., Zhou, T.Y.: Pfaffian solutions and nonlinear waves of a (3+1)- dimensional generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt...
  • 57. Kumar, S., Mohan, B.: A novel analysis of Cole-Hopf transformations in different dimensions, solitons, and rogue waves for a (2+1)-dimensional...
  • 58. Mohan, B., Kumar, S.: Generalization and analytic exploration of soliton solutions for nonlinear evolution equations via a novel symbolic...
  • 59. Liu, H.D., Tian, B., Feng, S.P., Chen, Y.Q., Zhou, T.Y.: Integrability, bilinearization, Bäcklund transformations and solutions for a...
  • 60. Subramanian, K.: Non-collisional dynamics of (2+1)-dimensional Broer-Kaup-Kupershmidt system. Nonlinear Dyn. 112(7), 5555–5563 (2024)