Result: Stationary problem related to the nonlinear Schrodinger equation on the unit ball
Title:
Stationary problem related to the nonlinear Schrodinger equation on the unit ball
Authors:
Source:
Nonlinearity (Bristol. Print). 25(8):2271-2301
Publisher Information:
Bristol: Institute of Physics, 2012.
Publication Year:
2012
Physical Description:
print, 56 ref
Original Material:
INIST-CNRS
Subject Terms:
Mathematics, Mathématiques, Theoretical physics, Physique théorique, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Analyse mathématique, Mathematical analysis, Equations aux dérivées partielles, Partial differential equations, Topologie. Variétés et complexes cellulaires. Analyse globale et analyse sur variétés, Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds, Analyse globale, analyse sur des variétés, Global analysis, analysis on manifolds, Physique, Physics, Generalites, General, Méthodes mathématiques en physique, Mathematical methods in physics, Divers, Other topics in mathematical methods in physics, Analyse non linéaire, Nonlinear analysis, análisis no lineal, Calcul 2 dimensions, Two-dimensional calculations, Condition aux limites, Boundary condition, Condiciones límites, Energie, Energy, Energía, Equation Schrödinger, Schrödinger equation, Ecuación Schrödinger, Equation non linéaire, Non linear equation, Ecuación no lineal, Equation onde, Wave equation, Ecuación onda, Espace état, State space, Espacio estado, Etat excité, Excited state, Estado excitado, Méthode espace état, State space method, Método espacio estado, Onde non linéaire, Non linear wave, Onda no lineal, Onde stationnaire, Standing wave, Onda estacionaria, Perturbation, Perturbación, Physique mathématique, Mathematical physics, Física matemática, Problème non linéaire, Nonlinear problems, Puissance, Power, Potencia, Simulation numérique, Numerical simulation, Simulación numérica, Stabilité linéaire, Linear stability, Estabilidad lineal, Stabilité numérique, Numerical stability, Estabilidad numérica, Symétrie, Symmetry, Simetría, 35J05, 35Q55, Boule unité, Condition Dirichlet, Non linéarité cubique
Document Type:
Academic journal
Article
File Description:
text
Language:
English
Author Affiliations:
Graduate School of Information Sciences, Tohoku University, 6-3-09 Aramaki-Aza-Aoba, Aoba-ku, Sendai 980-8579, Japan
Laboratoire de Mathémathiques, Reims University, BP 1039, 51687 Reims, France
Department of Mathematics, Hokkaido University, Kita 10, Nishi 8, Kita-ku, Sapporo 060-0810, Japan
Laboratoire de Mathémathiques, Reims University, BP 1039, 51687 Reims, France
Department of Mathematics, Hokkaido University, Kita 10, Nishi 8, Kita-ku, Sapporo 060-0810, Japan
ISSN:
0951-7715
Rights:
Copyright 2015 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics
Theoretical physics
Theoretical physics
Accession Number:
edscal.26259453
Database:
PASCAL Archive
Further Information
In this paper, we study the stability of standing waves for the nonlinear Schrödinger equation on the unit ball in ℝN with Dirichlet boundary condition. We generalize the result of Fibich and Merle (2001 Physica D 155 132―58), which proves the orbital stability of the least-energy solution with the cubic power nonlinearity in two space dimension. We also obtain several results concerning the excited states in one space dimension. Specifically, we show the linear stability of the first three excited states and we give a proof of the orbital stability of the kth excited state, restricting ourselves to the perturbation of the same symmetry as the kth excited state. Finally, our numerical simulations on the stability of the kth excited state are presented.