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TMF, 2021 Volume 209, Number 1, Pages 46–58 (Mi tmf10095)

Explicit breather solution of the nonlinear Schrödinger equation

R. Conteab

a Université Paris-Saclay, ENS Paris-Saclay, CNRS, Centre Borelli, Gif-sur-Yvette, France
b Department of Mathematics, The University of Hong Kong, Hong Kong

Abstract: We present a one-line closed-form expression for the three-parameter breather of the nonlinear Schrödinger equation. This provides an analytic proof of the time period doubling observed in experiments. The experimental check that some pulses generated in optical fibers are indeed such generalized breathers will be drastically simplified.

Keywords: modulational instability, nonlinear Schrödinger equation, nonlinear optics, breather, exact solutions.

PACS: 02.30.Hq, 02.30.Jr, 03.75.Kk, 03.75.Lm, 42.65.J, 42.65.-k

Received: 15.03.2021
Revised: 15.03.2021

DOI: 10.4213/tmf10095


 English version:
Theoretical and Mathematical Physics, 2021, 209:1, 1357–1366

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© Steklov Math. Inst. of RAS, 2024