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

Research output: Contribution to journalArticle

2 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)3295-3306
Number of pages12
JournalInternational Journal of Bifurcation and Chaos
Volume13
Issue number11
DOIs
StatePublished - Nov 2003

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Morse Index
Ginzburg-Landau Equation
Potential Well
Gradient Algorithm
Bifurcation Point
Equivariant
Galerkin
Small Parameter
Branching
Lemma
Trivial
Branch
Bifurcation
Classify
Numerical Solution
Symmetry
Bifurcation (mathematics)

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

  • General
  • Applied Mathematics

Cite this

Numerical solutions of a vector Ginzburg-Landau equation with a triple-well potential. / Neuberger, John M; Rice, Dennis R.; Swift, James W.

In: International Journal of Bifurcation and Chaos, Vol. 13, No. 11, 11.2003, p. 3295-3306.

Research output: Contribution to journalArticle

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