Non-synchronized solutions to nonlinear elliptic Schrödinger systems on a closed Riemannian manifold

Abstract

On a smooth, closed Riemannian manifold, we study the question of proportionality of components, also called synchronization, of vector-valued solutions to nonlinear elliptic Schrödinger systems with constant coefficients. In particular, we obtain bifurcation results showing the existence of branches of non-synchronized solutions emanating from the constant solutions.

References in corpus (6)

• Phase separation of Bose-Einstein condensates
• Exact soliton solutions, shape changing collisions and partially coherent solitons in coupled nonlinear Schroedinger equations
• Multipulse phases in k-mixtures of Bose-Einstein condensates
• Uniform bounds for strongly competing systems: the optimal Lipschitz case
• Proportionality of components, Liouville theorems and a priori estimates for noncooperative elliptic systems
• Yamabe systems, optimal partitions, and nodal solutions to the Yamabe equation