Jacobian-Elliptic-Function and Rogue-Periodic-Wave Solutions of a Fifth-Order Nonlinear Schrödinger Equation in an Optical Fiber

• Autores: Cheng-Cheng Wei, Bo Tian, Xin Zhao, Yu-Qi Chen
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 22, Nº 1, 2023
• Idioma: inglés
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• Resumen

  • Optical fiber communication becomes the main research direction in optical networking, computing, telecommunications and data communication. In an optical fiber, a fifth-order nonlinear Schrödinger equation describing the propagation of ultrashort optical pulses is studied in this paper. We give the Jacobian-elliptic-function solutions of that equation as the seed solutions. Based on the periodic background, we combine the nonlinearization of the spectral problem with the Darboux-transformation method to derive the rogue-periodic-wave solutions. When the coefficient α2 in that equation increases, the period and maximum amplitude of the onefold rogue-dn-periodic wave remain unchanged, while the minimum amplitude of the onefold rogue-dn-periodic wave rises; when the coefficient α1 or α3 in that equation increases, the maximum amplitude of the onefold rogue-dn-periodic wave remains unchanged, the minimum amplitude of the onefold rogue-dn-periodic wave decreases, while the period of the onefold rogue-dn-periodic becomes smaller. The conclusion of the twofold roguecn-periodic wave is the same as that of the onefold rogue-dn-periodic wave. When the coefficient α1 in that equation increases, the maximum amplitude of the onefold rogue-cn-periodic wave remains unchanged, the minimum amplitude of the onefold rogue-cn-periodic wave rises, while the period of the onefold rogue-cn-periodic wave becomes smaller; when the coefficient α2 in that equation increases, the period and maximum amplitude of the onefold rogue-cn-periodic wave remain unchanged, while the minimum amplitude of the onefold rogue-cn-periodic wave decreases; when the coefficient α3 in that equation increases, the maximum amplitude of the onefold rogue-cn-periodic wave remains unchanged, the minimum amplitude of the onefold rogue-cn-periodic wave decreases, while the period of the onefold rogue-cn-periodic wave becomes smaller.