A Radial Positive Solution For Linearly Coupled Nonlinear Schrodinger Systems

This paper is concerned with the following system linearly coupled by nonlinear Schrodinger equations where ε ∈ R is a parameter. This type of system arises when one considers standing wave solutions of the time-dependent N-coupled Schrodinger systems of the form This type of system describes some physical phenomenas such as nonlinear optics.We perform a Lyapunov - Schmidt reduction argument and construct a radial positive solution (u1,ε,…,uN,ε) which bifurcates from the semi-classical solution (U,0, …,0). Then, we prove the asymptotic behavior of the solution at infinity.