Article citationsMore>>

Carter, J.D. (2012) Plane Wave Solutions of a Dissipative Generalization of the Vector Nonlinear Schrödinger Equation. Mathematics and Computers in Simulation, 82, 1038-1046.
https://doi.org/10.1016/j.matcom.2010.07.032

has been cited by the following article:

• 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.