Geodesic
Long-time behavior of solutions to the derivative nonlinear Schrödinger equation for soliton-free initial data
Annales de l'I.H.P. Analyse non linéaire, Tome 35 (2018) no. 1, pp. 217-265

Voir la notice de l'article provenant de la source Numdam

The large-time behavior of solutions to the derivative nonlinear Schrödinger equation is established for initial conditions in some weighted Sobolev spaces under the assumption that the initial conditions do not support solitons. Our approach uses the inverse scattering setting and the nonlinear steepest descent method of Deift and Zhou as recast by Dieng and McLaughlin.

On établit le comportement au temps long des solutions de l'équation de Schrödinger nonlinéraire avec dérivée dans des espaces de Sobolev à poids, sous l'hypothèse que les conditions initiales ne supportent pas de solitons. Notre approche utilise l'inverse scattering et la méthode de la plus grande pente (“steepest descent”) nonlinéaire de Deift et Zhou revisitée par Dieng et McLaughlin.

DOI : 10.1016/j.anihpc.2017.04.002
Keywords: Riemann–Hilbert problem, Inverse scattering method, Nonlinear steepest descent method 
@article{AIHPC_2018__35_1_217_0,
     author = {Liu, Jiaqi and Perry, Peter A. and Sulem, Catherine},
     title = {Long-time behavior of solutions to the derivative nonlinear {Schr\"odinger} equation for soliton-free initial data},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {217--265},
     publisher = {Elsevier},
     volume = {35},
     number = {1},
     year = {2018},
     doi = {10.1016/j.anihpc.2017.04.002},
     mrnumber = {3739932},
     zbl = {1382.35271},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2017.04.002/}
}
TY  - JOUR
AU  - Liu, Jiaqi
AU  - Perry, Peter A.
AU  - Sulem, Catherine
TI  - Long-time behavior of solutions to the derivative nonlinear Schrödinger equation for soliton-free initial data
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2018
SP  - 217
EP  - 265
VL  - 35
IS  - 1
PB  - Elsevier
UR  - http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2017.04.002/
DO  - 10.1016/j.anihpc.2017.04.002
LA  - en
ID  - AIHPC_2018__35_1_217_0
ER  - 
%0 Journal Article
%A Liu, Jiaqi
%A Perry, Peter A.
%A Sulem, Catherine
%T Long-time behavior of solutions to the derivative nonlinear Schrödinger equation for soliton-free initial data
%J Annales de l'I.H.P. Analyse non linéaire
%D 2018
%P 217-265
%V 35
%N 1
%I Elsevier
%U http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2017.04.002/
%R 10.1016/j.anihpc.2017.04.002
%G en
%F AIHPC_2018__35_1_217_0
Liu, Jiaqi; Perry, Peter A.; Sulem, Catherine. Long-time behavior of solutions to the derivative nonlinear Schrödinger equation for soliton-free initial data. Annales de l'I.H.P. Analyse non linéaire, Tome 35 (2018) no. 1, pp. 217-265. doi: 10.1016/j.anihpc.2017.04.002

Cité par Sources :