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This paper originally appeared in Nonlinear Evolution Equations and Dynamical Systems NEEDS 94, a proceedings volume edited by Makhankov et. al. and published by World Scientific in 1995. To download a preprint of this paper, just click here.

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Macroscopic Behavior in the Ablowitz-Ladik Equations

Peter D. Miller
Program in Applied Mathematics
The University of Arizona
Tucson, AZ 85721 USA

Abstract:

Modulation theory is used to study the Ablowitz-Ladik equations. Exact multiphase wavetrain solutions are found, and local conservation laws are averaged to obtain a macroscopic description of this lattice problem.