@Article{JMS-49-2,
author = {Liu, Chuangye and V., Nguyen, Nghiem and Zhi-Qiang, Wang},
title = {Existence and Stability of Solitary Waves of an M-Coupled Nonlinear Schrödinger System},
journal = {Journal of Mathematical Study},
year = {2016},
volume = {49},
number = {2},
pages = {132--148},
abstract = {<p style="text-align: justify;">In this paper, the existence and stability results for ground state solutions of 
an m-coupled nonlinear Schrödinger system $$i\frac{∂}{∂ t}u_j+\frac{∂²}{∂x²}u_j+\sum\limits^m_{i=1}b_{ij}|u_i|^p|u_j|^{p-2}u_j=0,$$ are established, where $2 ≤ m, 2≤p&lt;3$ and $u_j$ are complex-valued functions of $(x,t) ∈ \mathbb{R}^2,
j=1,...,m$ and $b_{ij}$ are positive constants satisfying $b_{ij}=b_{ji}$. In contrast with other methods
used before to establish existence and stability of solitary wave solutions where the
constraints of the variational minimization problem are related to one another, our approach
here characterizes ground state solutions as minimizers of an energy functional
subject to independent constraints. The set of minimizers is shown to be orbitally stable
and further information about the structure of the set is given in certain cases.</p>},
issn = {2617-8702},
doi = {https://doi.org/10.4208/jms.v49n2.16.03},
url = {https://global-sci.com/article/87796/existence-and-stability-of-solitary-waves-of-an-m-coupled-nonlinear-schrodinger-system}
}