In this paper, we consider the transverse instability for a system of nonlinear Schrödinger equations on R × TL. Here, T L means the torus with a 2πL period. It was shown by Colin-Ohta  that this system on R has a stable standing wave. In this paper, we regard this standing wave as the standing wave of this system on R × T L. Then, we show that there exists the critical period Lσ which is the boundary between the stability and the instability of the standing wave on R × TL.
|Number of pages
|Discrete and Continuous Dynamical Systems - Series B
|Published - Mar 2014
All Science Journal Classification (ASJC) codes
- Discrete Mathematics and Combinatorics
- Applied Mathematics