Non-synchronized solutions to nonlinear elliptic Schr\"odinger systems on a closed Riemannian manifold

TL;DR

This paper investigates the existence of non-synchronized solutions in nonlinear elliptic Schrödinger systems on closed Riemannian manifolds, revealing bifurcation phenomena from constant solutions.

Contribution

It provides bifurcation results demonstrating the emergence of non-synchronized solutions, expanding understanding of solution structures in such systems.

Findings

Existence of bifurcation branches of non-synchronized solutions

Non-synchronized solutions emanate from constant solutions

Analysis on closed Riemannian manifolds

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 Schr\"odinger systems with constant coefficients. In particular, we obtain bifurcation results showing the existence of branches of non-synchronized solutions emanating from the constant solutions.