Stability of periodic traveling waves for the quadratic and cubic nonlinear Schr\"odinger equations
Sevdzhan Hakkaev, Iliya D. Iliev, Kiril Kirchev
TL;DR
This paper investigates the existence and stability of periodic traveling wave solutions in one-dimensional quadratic and cubic nonlinear Schrödinger equations, providing insights into their behavior and stability properties.
Contribution
It offers new results on the existence and stability criteria of periodic traveling waves for these specific nonlinear Schrödinger equations.
Findings
Existence of periodic traveling wave solutions established.
Stability conditions for these solutions derived.
Insights into the dynamics of nonlinear Schrödinger equations obtained.
Abstract
We study the existence and stability of periodic traveling-wave solutions for the quadratic and cubic nonlinear Schr\"odinger equations in one space dimension.
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Taxonomy
TopicsAdvanced Mathematical Physics Problems · Nonlinear Photonic Systems · Nonlinear Waves and Solitons