Stability of elliptic solutions to the defocusing fourth order nonlinear Schrödinger equation

Abstract

We study the stability of elliptic solutions to the integrable defocusing fourth order nonlinear Schrödinger (4NLS) equation with respect to subharmonic perturbations. With the help of the squared-eigenfunction connection, we prove the spectral stability by relating the Lax spectrum to the stability spectrum. We establish the orbital stability of elliptic solutions to the 4NLS equation by constructing a Lyapunov functional.