Numerical solutions of a vector Ginzburg-Landau equation with a triple-well potential

John M. Neuberger; Dennis R. Rice; James W. Swift

doi:10.1142/S0218127403008740

Numerical solutions of a vector Ginzburg-Landau equation with a triple-well potential

John M. Neuberger, Dennis R. Rice, James W. Swift

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

We numerically compute solutions to the vector Ginzburg-Landau equation with a triple-well potential. We use the Galerkin Newton Gradient Algorithm of Neuberger and Swift and bifurcation techniques to find solutions. With a small parameter, we find a Morse index 2 triple junction solution. This is the solution for which Flores, Padilla and Tonegawa gave an existence proof. We classify all of the solutions guaranteed to exist by the Equivariant Branching Lemma at the first bifurcation points of the trivial solutions. Guided by the symmetry analysis, we numerically compute the solution branches.

Original language	English (US)
Pages (from-to)	3295-3306
Number of pages	12
Journal	International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume	13
Issue number	11
DOIs	https://doi.org/10.1142/S0218127403008740
State	Published - Nov 2003

Keywords

Bifurcation theory
Equivariant branching lemma
Gradient Newton Galerkin algorithm (or GNGA)
Semilinear elliptic partial differential equation (or PDE)
Triple junction

ASJC Scopus subject areas

Modeling and Simulation
Engineering (miscellaneous)
General
Applied Mathematics

Access to Document

10.1142/S0218127403008740

Cite this

@article{e994bfbd57b348128f8897bb215114f4,

title = "Numerical solutions of a vector Ginzburg-Landau equation with a triple-well potential",

abstract = "We numerically compute solutions to the vector Ginzburg-Landau equation with a triple-well potential. We use the Galerkin Newton Gradient Algorithm of Neuberger and Swift and bifurcation techniques to find solutions. With a small parameter, we find a Morse index 2 triple junction solution. This is the solution for which Flores, Padilla and Tonegawa gave an existence proof. We classify all of the solutions guaranteed to exist by the Equivariant Branching Lemma at the first bifurcation points of the trivial solutions. Guided by the symmetry analysis, we numerically compute the solution branches.",

keywords = "Bifurcation theory, Equivariant branching lemma, Gradient Newton Galerkin algorithm (or GNGA), Semilinear elliptic partial differential equation (or PDE), Triple junction",

author = "Neuberger, {John M.} and Rice, {Dennis R.} and Swift, {James W.}",

note = "Funding Information: We wish to thank Prof. P. Padilla of UNAM for many helpful discussions. This work was partially supported by NSF grant DMS-0074326.",

year = "2003",

month = nov,

doi = "10.1142/S0218127403008740",

language = "English (US)",

volume = "13",

pages = "3295--3306",

journal = "International Journal of Bifurcation and Chaos in Applied Sciences and Engineering",

issn = "0218-1274",

publisher = "World Scientific Publishing Co. Pte Ltd",

number = "11",

}

TY - JOUR

T1 - Numerical solutions of a vector Ginzburg-Landau equation with a triple-well potential

AU - Neuberger, John M.

AU - Rice, Dennis R.

AU - Swift, James W.

N1 - Funding Information: We wish to thank Prof. P. Padilla of UNAM for many helpful discussions. This work was partially supported by NSF grant DMS-0074326.

PY - 2003/11

Y1 - 2003/11

N2 - We numerically compute solutions to the vector Ginzburg-Landau equation with a triple-well potential. We use the Galerkin Newton Gradient Algorithm of Neuberger and Swift and bifurcation techniques to find solutions. With a small parameter, we find a Morse index 2 triple junction solution. This is the solution for which Flores, Padilla and Tonegawa gave an existence proof. We classify all of the solutions guaranteed to exist by the Equivariant Branching Lemma at the first bifurcation points of the trivial solutions. Guided by the symmetry analysis, we numerically compute the solution branches.

AB - We numerically compute solutions to the vector Ginzburg-Landau equation with a triple-well potential. We use the Galerkin Newton Gradient Algorithm of Neuberger and Swift and bifurcation techniques to find solutions. With a small parameter, we find a Morse index 2 triple junction solution. This is the solution for which Flores, Padilla and Tonegawa gave an existence proof. We classify all of the solutions guaranteed to exist by the Equivariant Branching Lemma at the first bifurcation points of the trivial solutions. Guided by the symmetry analysis, we numerically compute the solution branches.

KW - Bifurcation theory

KW - Equivariant branching lemma

KW - Gradient Newton Galerkin algorithm (or GNGA)

KW - Semilinear elliptic partial differential equation (or PDE)

KW - Triple junction

UR - http://www.scopus.com/inward/record.url?scp=1442360406&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=1442360406&partnerID=8YFLogxK

U2 - 10.1142/S0218127403008740

DO - 10.1142/S0218127403008740

M3 - Article

AN - SCOPUS:1442360406

SN - 0218-1274

VL - 13

SP - 3295

EP - 3306

JO - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

JF - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

IS - 11

ER -

Numerical solutions of a vector Ginzburg-Landau equation with a triple-well potential

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this