TITLE:
On Two Types of Stability of Solutions to a Pair of Damped Coupled Nonlinear Evolution Equations
AUTHORS:
Mark Jones
KEYWORDS:
Nonlinear Schrödinger Equation, Stability, Capillary-Gravity Waves
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.14 No.5,
May
23,
2024
ABSTRACT: The stability of a set of spatially constant plane wave solutions to a pair of damped coupled nonlinear Schrödinger evolution equations is considered. The equations could model physical phenomena arising in fluid dynamics, fibre optics or electron plasmas. The main result is that any small perturbation to the solution remains small for all time. Here small is interpreted as being both in the supremum sense and the square integrable sense.