Vortex families near a spectral edge in the Gross-Pitaevskii equation with a two-dimensional periodic potential

被引：2

作者：

Dohnal, Tomas ^{[1
]}

Pelinovsky, Dmitry ^{[2
]}

机构：

[1] Karlsruhe Inst Technol, Fak Math, DE-76131 Karlsruhe, Germany

[2] McMaster Univ, Dept Math, Hamilton, ON L8S 4K1, Canada

来源：

PHYSICAL REVIEW E | 2012年 / 85卷 / 02期

基金：

加拿大自然科学与工程研究理事会;

关键词：

NONLINEAR ELLIPTIC PROBLEM; CONTINUOUS APPROXIMATION; GAP SOLITONS; BREATHERS; EXISTENCE;

D O I：

10.1103/PhysRevE.85.026605

中图分类号：

O35 [流体力学]; O53 [等离子体物理学];

学科分类号：

070204 ; 080103 ; 080704 ;

摘要：

We examine numerically vortex families near band edges of the Bloch wave spectrum for the Gross-Pitaevskii equation with two-dimensional periodic potentials and for the discrete nonlinear Schrodinger equation. We show that besides vortex families that terminate at a small distance from the band edges via fold bifurcations, there exist vortex families that are continued all the way to the band edges.

引用

页数：6

共 22 条

[1] ON MATHEMATICAL MODELS FOR BOSE-EINSTEIN CONDENSATES IN OPTICAL LATTICES [J].

Aftalion, Amandine ;

Helffer, Bernard .

REVIEWS IN MATHEMATICAL PHYSICS, 2009, 21 (02) :229-278

[2] From non-local gap solitary waves to bound states in periodic media [J].

Akylas, T. R. ;

Hwang, Guenbo ;

Yang, Jianke .

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2012, 468 (2137) :116-135

[3] Continuous approximation of breathers in one- and two-dimensional DNLS lattices [J].

Bambusi, D. ;

Penati, T. .

NONLINEARITY, 2010, 23 (01) :143-157

[4] Existence and continuous approximation of small amplitude breathers in 1D and 2D Klein-Gordon lattices [J].

Bambusi, Dario ;

Paleari, Simone ;

Penati, Tiziano .

APPLICABLE ANALYSIS, 2010, 89 (09) :1313-1334

[5] Coupled mode equations and gap solitons for the 2D Gross-Pitaevskii equation with a non-separable periodic potential [J].

Dohnal, Tomas ;

Uecker, Hannes .

PHYSICA D-NONLINEAR PHENOMENA, 2009, 238 (9-10) :860-879

[6] Coupled-Mode Equations and Gap Solitons in a Two-Dimensional Nonlinear Elliptic Problem with a Separable Periodic Potential [J].

Dohnal, Tomas ;

Pelinovsky, Dmitry ;

Schneider, Guido .

JOURNAL OF NONLINEAR SCIENCE, 2009, 19 (02) :95-131

[7] EXISTENCE AND BIFURCATION OF SOLUTIONS FOR NONLINEAR PERTURBATIONS OF THE PERIODIC SCHRODINGER-EQUATION [J].

HEINZ, HP ;

KUPPER, T ;

STUART, CA .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1992, 100 (02) :341-354

[8] Gap solitons and their linear stability in one-dimensional periodic media [J].

Hwang, Guenbo ;

Akylas, T. R. ;

Yang, Jianke .

PHYSICA D-NONLINEAR PHENOMENA, 2011, 240 (12) :1055-1068

[9] BAND-EDGE SOLITONS, NONLINEAR SCHRODINGER/GROSS-PITAEVSKII EQUATIONS, AND EFFECTIVE MEDIA [J].

Ilan, B. ;

Weinstein, M. I. .

MULTISCALE MODELING & SIMULATION, 2010, 8 (04) :1055-1101

[10]

Keller H.B., 1977, Applications of Bifurcation Theory, P359

← 1 2 3 →