Dissipation in Singular Blow-up Solutions of the Nonlinear Schroedinger Equation
Brenton LeMesurier

College of Charleston
Department of Mathematics

Energy transfer in plasma turbulence and from high-intensity laser beams
due to multi-photon absorption can be modelled by a Dissipative
perturbation of the Nonlinear Schroedinger Equation (DNSE), and similar
phenomena can ooccur in laser propagation.

Numerical study of near-singular solutions of the DNSE in the limit of
dissipation coefficient approaching zero suggest that sustained
dissipative behaviour is possible in parameter regimes where it was not
previously expected, related to singular solutions of the NSE, and
reveal dissipation in a rapid train of bursts despite the steady form of
the NSE limit. These solutions are related to special singular solutions
of the NSE having dissipation into a point singularity.
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