On Two Types of Stability of Solutions to a Pair of Damped Coupled Nonlinear Evolution Equations  

作　　者：Mark Jones Mark Jones(School of Computer Science and Mathematics, Kingston University, London, UK)

机构地区：[1]School of Computer Science and Mathematics, Kingston University, London, UK

出　　处：《Advances in Pure Mathematics》2024年第5期354-366,共13页理论数学进展（英文）

摘　　要：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.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.

关 键 词：Nonlinear Schrödinger Equation STABILITY Capillary-Gravity Waves 

分 类 号：O17[理学—数学]