Dispersive blow-up for nonlinear Schrodinger equations revisited

被引：36

作者：

Bona, J. L. ^{[1
]}

Ponce, G. ^{[2
]}

Saut, J-C ^{[3
]}

Sparber, C. ^{[1
]}

机构：

[1] Univ Illinois, Dept Math Stat & Comp Sci, Chicago, IL 60607 USA

[2] Univ Calif Santa Barbara, Dept Math, Santa Barbara, CA 93106 USA

[3] Univ Paris 11, UMR 8628, Math Lab, F-91405 Orsay, France

来源：

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2014年 / 102卷 / 04期

基金：

美国国家科学基金会;

关键词：

Nonlinear Schrodinger equation; Dispersion; Finite time blow up; Rogue waves; Global smoothing estimates; GROSS-PITAEVSKII EQUATION; POINTWISE CONVERGENCE; TRAVELING-WAVES; CAUCHY-PROBLEM; SCATTERING;

D O I：

10.1016/j.matpur.2014.02.006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The possibility of finite-time, dispersive blow-up for nonlinear equations of Schrodinger type is revisited. This mathematical phenomena is one of the conceivable explanations for oceanic and optical rogue waves. In dimension one, the fact that dispersive blow up does occur for nonlinear Schrodinger equations already appears in [9]. In the present work, the existing results are extended in several ways. In one direction, the theory is broadened to include the Davey-Stewartson and Gross-Pitaevskii equations. In another, dispersive blow up is shown to obtain for nonlinear Schrodinger equations in spatial dimensions larger than one and for more general power-law nonlinearities. As a by-product of our analysis, a sharp global smoothing estimate for the integral term appearing in Duhamel's formula is obtained. (C) 2014 Elsevier Masson SAS. All rights reserved.

引用

页码：782 / 811

页数：30

共 50 条

[21] THE LIMIT OF BLOW-UP DYNAMICS SOLUTIONS FOR A CLASS OF NONLINEAR CRITICAL SCHRODINGER EQUATIONS
Jean-Jacques, N'takpe
Blin, L. Boua Sobo
Halima, Nachid
Gnowille, Kambire D.
ADVANCES IN DIFFERENTIAL EQUATIONS AND CONTROL PROCESSES, 2024, 31 (02): : 207 - 238
[22] Blow-up in nonlinear heat equations
Dejak, Steven
Gang, Zhou
Sigal, Israel Michael
Wang, Shuangcai
ADVANCES IN APPLIED MATHEMATICS, 2008, 40 (04) : 433 - 481
[23] Blow－Up　and　Mass　Concentration　of　Solutions　to　the　Cauchy　Problem　for　Nonlinear　Schrodinger　Equations
秦玉明
数学季刊, 1994, (02) : 18 - 24
[24] Blow-up for the stochastic nonlinear Schrodinger equations with quadratic potential and additive noise
Meng, Lixin
Li, Jingyu
Tao, Jian
BOUNDARY VALUE PROBLEMS, 2015,
[25] BLOW-UP, GLOBAL EXISTENCE AND STANDING WAVES FOR THE MAGNETIC NONLINEAR SCHRODINGER EQUATIONS
Gan, Zaihui
Zhang, Jian
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2012, 32 (03) : 827 - 846
[26] Stochastic nonlinear Schrodinger equations: No blow-up in the non-conservative case
Barbu, Viorel
Roeckner, Michael
Zhang, Deng
JOURNAL OF DIFFERENTIAL EQUATIONS, 2017, 263 (11) : 7919 - 7940
[27] Blow-up of the solutions for the initial-boundary problems of the nonlinear Schrodinger equations
Wang, FB
APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION, 2000, 21 (11) : 1338 - 1340
[28] Monotonicity properties of the blow-up time for nonlinear Schrodinger equations: Numerical evidence
Besse, Christophe
Carles, Remi
Mauser, Norbert J.
Stimming, Hans Peter
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2008, 9 (01): : 11 - 36
[29] Finite difference approximation for nonlinear Schrodinger equations with application to blow-up computation
Saito, Norikazu
Sasaki, Takiko
JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS, 2016, 33 (02) : 427 - 470
[30] A note on blow-up criteria for a class of nonlinear dispersive wave equations with dissipation
Xijun Deng
Monatshefte für Mathematik, 2021, 194 : 503 - 512

← 1 2 3 4 5 →