Instability of standing waves for a system of nonlinear Schr\"odinger equations in a degenerate case
Shotaro Kawahara, Masahito Ohta
TL;DR
This paper investigates the stability and instability of standing wave solutions in a one-dimensional nonlinear Schrödinger system with cubic interactions, focusing on both degenerate and non-degenerate cases.
Contribution
It provides a detailed analysis of the orbital stability and instability of semitrivial standing waves in degenerate and non-degenerate scenarios.
Findings
Stability results for non-degenerate cases.
Instability results for degenerate cases.
Characterization of conditions leading to stability or instability.
Abstract
We study a system of nonlinear Schr\"odinger equations with cubic interactions in one space dimension. The orbital stability and instability of semitrivial standing wave solutions are studied for both non-degenerate and degenerate cases.
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Taxonomy
TopicsNonlinear Photonic Systems · Advanced Mathematical Physics Problems · Nonlinear Dynamics and Pattern Formation