https://doi.org/10.1140/epjd/e2015-60212-7
Regular Article
Spatiotemporal wave-train instabilities in nonlinear Schrödinger equation: revisited
1 Laboratoire de Physique des Lasers,
Atomes et Molécules, CNRS UMR 8523, Université de Lille Sciences et Technologies,
59655 Villeneuve
d’ Ascq Cedex,
France
2 ICube, CNRS UMR 7357, Université de
Strasbourg, 2 rue
Boussingault, 67000
Strasbourg,
France
a e-mail: saliya.coulibaly@univ-lille1.fr
Received:
3
April
2015
Received in final form:
10
June
2015
Published online:
28
July
2015
A complete description of properties of the wave-train bifurcating from unstable basic oscillatory states (CW nonlinear stationary states) of the nonlinear Schrödinger equation are studied in the moving frames of reference as an initial value problem and using the methods of absolute and convective instabilities. The predictions are in excellent agreement with numerical solutions and may contribute understanding the nonlinear Schrödinger equation complex dynamics under various initial conditions including, localized and/or noisy initial conditions.
Key words: Optical Phenomena and Photonics
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2015
