The Stability Spectrum for Elliptic Solutions to the Focusing NLS Equation
arXiv:1610.08539 · doi:10.1016/j.physd.2017.01.004
Abstract
We present an analysis of the stability spectrum of all stationary elliptic-type solutions to the focusing Nonlinear Schrödinger equation (NLS). An analytical expression for the spectrum is given. From this expression, various quantitative and qualitative results about the spectrum are derived. Specifically, the solution parameter space is shown to be split into four regions of distinct qualitative behavior of the spectrum. Additional results on the stability of solutions with respect to perturbations of an integer multiple of the period are given, as well as a procedure for approximating the greatest real part of the spectrum.
36 pages, 15 figures
References in corpus (3)
Cited by in corpus (7)
- The Stability Spectrum for Elliptic Solutions to the Focusing NLS Equation
- Observation of modulation instability and rogue breathers on stationary periodic waves
- The Stability Spectrum for Elliptic Solutions to the Sine-Gordon Equation
- Stability of elliptic function solutions for the focusing modified KdV equation
- Elliptic finite-band potentials of a non-self-adjoint Dirac operator
- Periodic traveling waves in the ϕ^4 model: Instability, stability and localized structures
- Rigorous justification of the Whitham modulation theory for equations of NLS type