Asymptotic behavior in time of solution to the nonlinear Schrödinger equation with higher order anisotropic dispersion

Jean-Claude Saut; Jun-Ichi Segata

doi:10.3934/dcds.2019009

Article Contents

2019, Volume 39, Issue 1: 219-239. Doi: 10.3934/dcds.2019009

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Asymptotic behavior in time of solution to the nonlinear Schrödinger equation with higher order anisotropic dispersion

Jean-Claude Saut^1, and
Jun-Ichi Segata^2,

1.
Laboratoire de Mathématiques, CNRS and Université Paris-Sud, 91405 Orsay, France
2.
Mathematical Institute, Tohoku University, 6-3, Aoba, Aramaki, Aoba-ku, Sendai 980-8578, Japan

Received: October 2017

Revised: March 2018

Published online: January 2019

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Abstract

We consider the asymptotic behavior in time of solutions to the nonlinear Schrödinger equation with fourth order anisotropic dispersion (4NLS) which describes the propagation of ultrashort laser pulses in a medium with anomalous time-dispersion in the presence of fourth-order time-dispersion. We prove existence of a solution to (4NLS) which scatters to a solution of the linearized equation of (4NLS) as $t\to∞$.

Keywords:

Schrödinger equation with higher order dispersion,
scattering problem.

Mathematics Subject Classification: Primary: 35Q55; Secondary: 35B40.

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References

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