Segregated vector solutions for linearly coupled nonlinear Schrodinger systems Chang-Shou LinShuangjie Peng 35J60segregationconcentrationmulti-bump solutionsphase seperationsNonlinear Schrodinger equation We consider the system linearly coupled by nonlinear Schr\"odinger equations in $\R^3$: \[ \left\{ \begin{array}{ll} -\Delta u_j+u_j=u^3_j-\va\sum\limits_{i\neq j}^N u_i,\hspace{2mm} x\in \R^3, \vspace{0.2cm}\\ u_j\in H^1(\R^3),\quad j=1,\cdots,N, \end{array} \right. \] where $\va\in\R$ 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 $\ell\ge 2$, we construct a nonradial vector solution of segregated type, with two components having exactly $\ell$ positive bumps for $\va>0$ sufficiently small. We also give an explicit description of the characteristic features of the vector solutions. Indiana University Mathematics Journal 2014 text pdf 10.1512/iumj.2014.63.5310 10.1512/iumj.2014.63.5310 en Indiana Univ. Math. J. 63 (2014) 939 - 967 state-of-the-art mathematics http://iumj.org/access/