The Fourth-order dispersive nonlinear Schr\"odinger equation: orbital stability of a standing wave
F\'abio Natali, Ademir Pastor
TL;DR
This paper proves the orbital stability of a standing wave solution for a one-dimensional fourth-order dispersive cubic nonlinear Schrödinger equation using a Lyapunov function within the Hamiltonian framework.
Contribution
It establishes the orbital stability of a specific standing wave for the fourth-order dispersive nonlinear Schrödinger equation, a novel result in this context.
Findings
Orbital stability of the standing wave is proven.
A Lyapunov function is constructed for the proof.
The stability is shown in the energy space.
Abstract
Considered in this report is the one-dimensional fourth-order dispersive cubic nonlinear Schr\"odinger equation with mixed dispersion. Orbital stability, in the energy space, of a particular standing-wave solution is proved in the context of Hamiltonian systems. The main result is established by constructing a suitable Lyapunov function.
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Taxonomy
TopicsAdvanced Mathematical Physics Problems · Nonlinear Photonic Systems · Nonlinear Waves and Solitons