Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Whitham equations for the defocusing nonlinear Schrodinger
  equation with step initial data   The behavior of solutions of the finite-genus Whitham equations for the weak
dispersion limit of the defocusing nonlinear Schrodinger equation is
investigated analytically and numerically for piecewise-constant initial data.
In particular, the dynamics of constant-amplitude initial conditions with one
or more frequency jumps (i.e., piecewise linear phase) are considered. It is
shown analytically and numerically that, for finite times, regions of
arbitrarily high genus can be produced; asymptotically with time, however, the
solution can be divided into expanding regions which are either of genus-zero,
genus-one or genus-two type, their precise arrangement depending on the
specifics of the initial datum given. This behavior should be compared to that
of the Korteweg-deVries equation, where the solution is devided into the
regions which are either genus-zero or genus-one asymptotically. Finally, the
potential application of these results to the generation of short optical
pulses is discussed: the method proposed takes advantage of nonlinear
compression via appropriate frequency modulation, and allows control of both
the pulse amplitude and its width, as well as the distance along the fiber at
which the pulse is produced.

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The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
2
The categories of this paper are: math
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg