Title: Segregated vector solutions for linearly coupled nonlinear Schrodinger systems
Authors: Chang-shou Lin and Shuangjie Peng
Issue: Volume 63 (2014), Issue 4, 939-967
Abstract:
![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.](https://iumj.s3-us-west-2.amazonaws.com/abstracts/5310.png)
Title: Segregated vector solutions for linearly coupled nonlinear Schrodinger systems
Authors: Chang-shou Lin and Shuangjie Peng
Issue: Volume 63 (2014), Issue 4, 939-967
Abstract: