On Two Types of Stability of Solutions to a Pair of Damped Coupled Nonlinear Evolution Equations ()
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.
Share and Cite:
Jones, M. (2024) On Two Types of Stability of Solutions to a Pair of Damped Coupled Nonlinear Evolution Equations.
Advances in Pure Mathematics,
14, 354-366. doi:
10.4236/apm.2024.145020.
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