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.
- Bifurcation theory
- Equivariant branching lemma
- Gradient Newton Galerkin algorithm (or GNGA)
- Semilinear elliptic partial differential equation (or PDE)
- Triple junction
ASJC Scopus subject areas
- Applied Mathematics