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Analytic representation of DM-solitons in the NLS equation

Wednesday 14th November 2001 - 11:00 to 12:00
INI Seminar Room 1
A simple exact formula is derived for the profile of the optical pulse propagating over a DM fibre with zero mean dispersion. The dissipation is neglected and dispersion is assumed to be constant along the adjacent legs of the waveguide, thus providing the applicability of the integrable NLS models within each leg. The formula describes a class of solutions called dispersion managed solitons (DM solitons),which are periodic along the waveguide and exponentially localised in time.

DM solitons are parametrised by a certain class of spectral data, specified from numerical simulations. Using a related Riemann-Hilbert problem we reconstruct a profile of DM soliton from the given spectral data. For long enough legs the leading term of DM soliton is found in explicit form by "asymptotic undressing" of the Riemann-Hilbert problem. The analytical results are compared with numerical simulations.

University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons