1207.1989 (Thomas Bartsch)

Locked solutions of coupled Gross-Pitaevskii equations    [PDF]

Thomas Bartsch

We consider the system -\Delta u_j + a(x)u_j = \mu_j u_j^3 + \be\sum_{k\ne j}u_k^2u_j,\ u_j>0, \qquad j=1,...,n, on a possibly unbounded domain $\Om\subset\R^N$, $N\le3$, with Dirichlet boundary conditions. The system appears in nonlinear optics and in the analysis of mixtures of Bose-Einstein condensates. Two components $u_i,u_j$ are said to be locked if $u_i/u_j$ is constant. The main results are concerned with the bifurcation of solutions $(u_1,...,u_n)$ where some components are locked from a branch where all solutions are locked. The bifurcation parameter is $\be$.

View original: http://arxiv.org/abs/1207.1989