A UNIVERSAL ASYMPTOTIC REGIME IN THE HYPERBOLIC NONLINEAR SCHRODINGER EQUATION

被引：8

作者：

Ablowitz, Mark J. ^{[1
]}

Ma, Yi-Ping ^{[1
,2
]}

Rumanov, Igor ^{[1
]}

机构：

[1] Univ Colorado, Dept Appl Math, Boulder, CO 80309 USA

[2] Northumbria Univ, Dept Math Phys & Elect Engn, Newcastle Upon Tyne NE1 8ST, Tyne & Wear, England

来源：

SIAM JOURNAL ON APPLIED MATHEMATICS | 2017年 / 77卷 / 04期

基金：

美国国家科学基金会;

关键词：

nonlinear waves; hyperbolic NLS equation; long-time asymptotics; NORMAL DISPERSION; X-WAVES; COLLAPSE; INSTABILITY; EVOLUTION; SOLITONS; LIGHT; BEAMS;

D O I：

10.1137/16M1099960

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The appearance of a fundamental long-time asymptotic regime in the two space-one time dimensional hyperbolic nonlinear Schrodinger (HNLS) equation is discussed. Based on analytical and numerical simulations, a wide range of initial conditions corresponding to initial lumps of moderate energy are found to approach a quasi-self-similar solution. Even relatively large initial amplitudes, which imply strong nonlinear effects, eventually lead to local structures resembling those of the self-similar solution, with appropriate small modifications. This solution has aspects that suggest it is a universal attractor emanating from a wide range of initial data.

引用

页码：1248 / 1268

页数：21

共 51 条

[1]

ABLOWITZ M., 2016, PREPRINT

[2] Nonlinear temporal-spatial surface plasmon polaritons [J].

Ablowitz, M. J. ;

Butler, S. T. J. .

OPTICS COMMUNICATIONS, 2014, 330 :49-55

[3]

Ablowitz M.J., 1991, Nonlinear Evolution Equations and Inverse Scattering

[4]

Ablowitz M. J., 1981, STUD APPL NUMER MATH, V4

[5] NOTE ON MIURA TRANSFORMATION [J].

ABLOWITZ, MJ ;

KRUSKAL, M ;

SEGUR, H .

JOURNAL OF MATHEMATICAL PHYSICS, 1979, 20 (06) :999-1003

[6]

ABLOWITZ MJ, 1977, STUD APPL MATH, V57, P13

[7] EVOLUTION OF PACKETS OF WATER-WAVES [J].

ABLOWITZ, MJ ;

SEGUR, H .

JOURNAL OF FLUID MECHANICS, 1979, 92 (JUN) :691-715

[8] Hyperbolic shock waves of the optical self-focusing with normal group-velocity dispersion -: art. no. 153902 [J].

Bergé, L ;

Germaschewski, K ;

Grauer, R ;

Rasmussen, JJ .

PHYSICAL REVIEW LETTERS, 2002, 89 (15) :153902/1-153902/4

[9] Wave collapse in physics: principles and applications to light and plasma waves [J].

Berge, L .

PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS, 1998, 303 (5-6) :259-370

[10] Defocusing regimes of nonlinear waves in media with negative dispersion [J].

Berge, L ;

Kuznetsov, EA ;

Rasmussen, JJ .

PHYSICAL REVIEW E, 1996, 53 (02) :R1340-R1343

← 1 2 3 4 5 6 →