Modified Nonlinear Schrödinger Equation for Nonlinear Waves in Optical Fibres
K. Murawski
Department of Mathematical Sciences, University of St Andrews, St Andrews, KY16 9SS, Scotland
Received: August 30, 1989; in revised version: April 16, 1991
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A new model equation governing the propagation of nonlinear pulses in optical fibres has been derived on the assumption of a saturated nonlinearity of the refractive index. This equation is a combination of the exponential nonlinear Schrödinger equation and the derivative one. It is valid for the long fibres. A modulational stability has been calculated to find out a cut-off in an angular frequency of a carrier wave. Moreover, it has been shown that the equation possesses family of stationary solutions. An initial value problem has been discussed on the basis of the implicit pseudo-spectral scheme.
DOI: 10.12693/APhysPolA.80.485
PACS numbers: 03.40.Kf, 42.65.-k, 52.35.Mw