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- W2012608378 abstract "We consider the system $${-Delta{u}_{j} + a(x)u_{j} = mu_{j}u^{3}_{j} + beta sum_{k neq j} u^{2}_{k}u_{j}}$$ , u j > 0, j = 1, . . . , n, on a possibly unbounded domain $${Omega subset mathbb{R}^{N}, N leq 3}$$ , with Dirichlet boundary conditions. The system appears in nonlinear optics and in the analysis of mixtures of Bose–Einstein condensates. We consider the self-focussing (attractive self-interaction) case $${mu_{1}, ldots, mu_{n} > 0}$$ and take $${beta in mathbb{R}}$$ as bifurcation parameter. There exists a branch of positive solutions with uj/uk being constant for all $${j, k in {1, ldots, n}}$$ . The main results are concerned with the bifurcation of solutions from this branch. Using a hidden symmetry we are able to prove global bifurcation even when the linearization has even-dimensional kernel (which is always the case when n > 1 is odd)." @default.
- W2012608378 created "2016-06-24" @default.
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- W2012608378 date "2013-03-01" @default.
- W2012608378 modified "2023-10-14" @default.
- W2012608378 title "Bifurcation in a multicomponent system of nonlinear Schrödinger equations" @default.
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- W2012608378 doi "https://doi.org/10.1007/s11784-013-0109-4" @default.
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