COUPLED NLS EQUATIONS FOR COUNTER PROPAGATING WAVES IN SYSTEMS WITH REFLECTION SYMMETRY

The amplitude of a wavetrain in a dispersive system generally evolves according to the cubic nonlinear Schrodinger (NLS) equation. In a reflection-symmetric system, the interaction of right and left travelling wavetrains with amplitudes epsilon-A + (zeta +, T2) and epsilon-A - (zeta-, T2) is described by two nonlinear Schrodinger equations with mean field coupling: +/- 2i-partial-A +/- /partial-T2 + (d2-omega/dk2) x partial-2 A +/- /partial-zeta +/- 2 = mu +/- A +/- + alpha-A +/- \A +/- \2. The independent variables are defined by zeta +/- = epsilon (c(g)t +/- chi), T2 = epsilon-2-t and the coupling arises through mu +/- = beta[ (1/P -/+) integral-o/p -/+ \A -/+ \2 d-zeta -/+]. The analysis is applied to electromagnetic wave propagation in an optical fibre.