Abstract
The amplitude of a wavetrain in a dispersive system generally evolves according to the cubic nonlinear Schrödinger (NLS) equation. In a reflection-symmetric system, the interaction of right and left travelling wavetrains with amplitudes ϵA +( ξ +, T 2) and ϵA -( ξ -, T 2) is described by two nonlinear Schrödinger equations with mean field coupling: ±2 i∂A ±/∂T 2+( d 2ω/ dk 2)×∂ 2A ±/∂ξ ±2=μ ±A ±+αA ±¦A ±¦ 2 . The independent variables are defined by ξ ±= ϵ( c g t∓ x ), T 2= ϵ 2 t and the coupling arises through μ ±≡β[(1/P ∓)∫ P∓ 0¦A ∓¦ 2 dξ ∓] . The analysis is applied to electromagnetic wave propagation in an optical fibre.
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