Segregated Vector Solutions for Linearly Coupled Nonlinear Schrodinger Systems

We consider the system linearly coupled by nonlinear Schrodinger equations in R-3: [GRAPHICS] where epsilon is an element of R is a coupling constant. This type of system arises in particular in models in nonlinear N-core fiber. We then examine how the linear coupling affects the solution structure. When N = 2, 3, for any prescribed integer l >= 2, we construct a nonradial vector solution of segregated type, with two components having exactly l positive bumps for epsilon > 0 sufficiently small. We also give an explicit description of the characteristic features of the vector solutions.