Averaging of dispersion managed nonlinear Schrödinger equations. (7th April 2022)

• Record Type: Journal Article
• Authors: Choi, Mi-Ran; Lee, Young-Ran
• Is Part Of: Nonlinearity. Volume 35:Number 4(2022)
• Page Start: 2121
• Page End: 2133
• Publication Date: 2022-04-07
• Subjects: dispersion managed nonlinear Schrödinger equation -- averaging -- global existence; 35A01 -- 35B27 -- 35Q55 -- 35Q60; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/ac5464
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: We consider the dispersion managed power-law nonlinear Schrödinger (DM NLS) equations with a small parameter ɛ > 0 and the averaged equation, which are used in optical fiber communications. We prove that the solutions of DM NLS equations converge to the solution of the averaged equation in H 1 ( R ) as ɛ goes to zero. Meanwhile, in the positive average dispersion, we obtain the global existence of the solution to DM NLS equation in H 1 ( R ) for sufficiently small ɛ > 0, even when the exponent of the nonlinearity is beyond the mass-critical power.