Propagation and reflection of singularities for the nonlinear Schrodinger equation

被引：6

作者：

Szeftel, J ^{[1
]}

机构：

[1] Univ Paris 13, LAGA UMR 7539, Inst Galilee, F-93430 Villetaneuse, France

来源：

ANNALES DE L INSTITUT FOURIER | 2005年 / 55卷 / 02期

关键词：

D O I：

10.5802/aif.2108

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We construct a paradifferential calculus well-suited to the Schrodinger equation which allows us to prove a result on propagation of singularities for the nonlinear Schrodinger equation by adapting Bony's method. We also construct the tangential version of the previous paradifferential calculus which allows us to prove a result on reflection of singularities for the nonlinear Schrodinger equation. We then use this result to compute the Dirichlet to Neumann map of the nonlinear Schrodinger equation.

引用

页码：573 / +

页数：101

共 50 条

[1] Reflection of singularities for the Schrodinger equation
Szeftel, J
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2004, 29 (5-6) : 707 - 761
[2] Nonlinear Schrodinger Equation with Singularities
Dugandzija, Nevena
Vojnovic, Ivana
QUALITATIVE PROPERTIES OF DISPERSIVE PDES, 2022, 52 : 91 - 107
[3] Well posedness of the nonlinear Schrodinger equation with isolated singularities
Cacciapuoti, Claudio
Finco, Domenico
Noja, Diego
JOURNAL OF DIFFERENTIAL EQUATIONS, 2021, 305 : 288 - 318
[4] On the formation of singularities in solutions of the critical nonlinear Schrodinger equation
Perelman, G
ANNALES HENRI POINCARE, 2001, 2 (04): : 605 - 673
[5] STABILITY OF ISOTROPIC SINGULARITIES FOR THE NONLINEAR SCHRODINGER-EQUATION
LANDMAN, MJ
PAPANICOLAOU, GC
SULEM, C
SULEM, PL
WANG, XP
PHYSICA D, 1991, 47 (03): : 393 - 415
[6] FORMATION OF SINGULARITIES IN SOLUTIONS OF THE NONLINEAR SCHRODINGER-EQUATION
NAWA, H
PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 1991, 67 (01) : 29 - 34
[7] On the reflection of solitons of the cubic nonlinear Schrodinger equation
Katsaounis, Theodoros
Mitsotakis, Dimitrios
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2018, 41 (03) : 1013 - 1018
[8] Dissipation at singularities of the nonlinear Schrodinger equation through limits of regularisations
LeMesurier, BJ
PHYSICA D-NONLINEAR PHENOMENA, 2000, 138 (3-4) : 334 - 343
[9] Dissipation at singularities of the nonlinear Schrodinger equation through limits of regularizations
LeMesurier, Brenton J.
Physica D: Nonlinear Phenomena, 2000, 138 (03) : 334 - 343
[10] Any-order propagation of the nonlinear Schrodinger equation
Strauch, Frederick W.
PHYSICAL REVIEW E, 2007, 76 (04):

← 1 2 3 4 5 →