Nonlinear Schrödinger equations with a four-well potential in two dimensions: Bifurcations and stability analysis

C. Wang; G. Theocharis; P. G. Kevrekidis; N. Whitaker; D. J. Frantzeskakis; B. A. Malomed

doi:10.1007/978-90-481-9884-9_22

Nonlinear Schrödinger equations with a four-well potential in two dimensions: Bifurcations and stability analysis

C. Wang, G. Theocharis, P. G. Kevrekidis, N. Whitaker, D. J. Frantzeskakis, B. A. Malomed

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

We report a full bifurcation diagram for trapped states in the two-dimensional (2D) nonlinear Schrödinger (NLS) equation with a symmetric four-well potential. Starting from the linear limit, we use a four-mode approximation to derive a system of ordinary differential equations, which makes it possible to trace the evolution of all trapped stationary modes, and thus to identify different branches of solutions bifurcating in the full NLS model. Their stability is examined within the framework of the linear stability analysis.

Original language	English
Title of host publication	Nonlinear Science and Complexity
Publisher	Springer Netherlands
Pages	173-179
Number of pages	7
ISBN (Print)	9789048198832
DOIs	https://doi.org/10.1007/978-90-481-9884-9_22
State	Published - 2011
Externally published	Yes

Keywords

Double-well potentials
Few-mode reduction
Linear stability analysis
Nonlinear Schrödinger equations

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10.1007/978-90-481-9884-9_22

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title = "Nonlinear Schr{\"o}dinger equations with a four-well potential in two dimensions: Bifurcations and stability analysis",

abstract = "We report a full bifurcation diagram for trapped states in the two-dimensional (2D) nonlinear Schr{\"o}dinger (NLS) equation with a symmetric four-well potential. Starting from the linear limit, we use a four-mode approximation to derive a system of ordinary differential equations, which makes it possible to trace the evolution of all trapped stationary modes, and thus to identify different branches of solutions bifurcating in the full NLS model. Their stability is examined within the framework of the linear stability analysis.",

keywords = "Double-well potentials, Few-mode reduction, Linear stability analysis, Nonlinear Schr{\"o}dinger equations",

author = "C. Wang and G. Theocharis and Kevrekidis, {P. G.} and N. Whitaker and Frantzeskakis, {D. J.} and Malomed, {B. A.}",

year = "2011",

doi = "10.1007/978-90-481-9884-9_22",

language = "אנגלית",

isbn = "9789048198832",

pages = "173--179",

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publisher = "Springer Netherlands",

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TY - CHAP

T1 - Nonlinear Schrödinger equations with a four-well potential in two dimensions

T2 - Bifurcations and stability analysis

AU - Wang, C.

AU - Theocharis, G.

AU - Kevrekidis, P. G.

AU - Whitaker, N.

AU - Frantzeskakis, D. J.

AU - Malomed, B. A.

PY - 2011

Y1 - 2011

N2 - We report a full bifurcation diagram for trapped states in the two-dimensional (2D) nonlinear Schrödinger (NLS) equation with a symmetric four-well potential. Starting from the linear limit, we use a four-mode approximation to derive a system of ordinary differential equations, which makes it possible to trace the evolution of all trapped stationary modes, and thus to identify different branches of solutions bifurcating in the full NLS model. Their stability is examined within the framework of the linear stability analysis.

AB - We report a full bifurcation diagram for trapped states in the two-dimensional (2D) nonlinear Schrödinger (NLS) equation with a symmetric four-well potential. Starting from the linear limit, we use a four-mode approximation to derive a system of ordinary differential equations, which makes it possible to trace the evolution of all trapped stationary modes, and thus to identify different branches of solutions bifurcating in the full NLS model. Their stability is examined within the framework of the linear stability analysis.

KW - Double-well potentials

KW - Few-mode reduction

KW - Linear stability analysis

KW - Nonlinear Schrödinger equations

UR - http://www.scopus.com/inward/record.url?scp=84895371636&partnerID=8YFLogxK

U2 - 10.1007/978-90-481-9884-9_22

DO - 10.1007/978-90-481-9884-9_22

M3 - פרק

AN - SCOPUS:84895371636

SN - 9789048198832

SP - 173

EP - 179

BT - Nonlinear Science and Complexity

PB - Springer Netherlands

ER -

Nonlinear Schrödinger equations with a four-well potential in two dimensions: Bifurcations and stability analysis

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Keywords

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