Orbital stability of spatially synchronized solitary waves of an m-coupled nonlinear Schrödinger system (Q2832698)

The paper addresses a system of \(m\) one-dimensional nonlinear Schrödinger equations with the attractive sign of the nonlinearity. The equations are coupled by cubic cross-phase-modulation terms, which is represented by a symmetric matrix of the interaction coefficients. The object of the analysis are \(m\)-component synchronized solitons, i.e., a soliton complex with the single intrinsic frequency, and will all the components proportional to each other. In spite of the relative simplicity of such synchronized complexes, their existence and stability was previously rigorously established only for \(m=2\). The present paper provides an explicit existence and stability proof for all \(m\geq 3\). Variational methods are used for the proof.