Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Shock waves in the dissipative Toda lattice   We consider the propagation of a shock wave (SW) in the damped Toda lattice.
The SW is a moving boundary between two semi-infinite lattice domains with
different densities. A steadily moving SW may exist if the damping in the
lattice is represented by an ``inner'' friction, which is a discrete analog of
the second viscosity in hydrodynamics. The problem can be considered
analytically in the continuum approximation, and the analysis produces an
explicit relation between the SW's velocity and the densities of the two
phases. Numerical simulations of the lattice equations of motion demonstrate
that a stable SW establishes if the initial velocity is directed towards the
less dense phase; in the opposite case, the wave gradually spreads out. The
numerically found equilibrium velocity of the SW turns out to be in a very good
agreement with the analytical formula even in a strongly discrete case. If the
initial velocity is essentially different from the one determined by the
densities (but has the correct sign), the velocity does not significantly
alter, but instead the SW adjusts itself to the given velocity by sending
another SW in the opposite direction.

18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
2
The categories of this paper are: math
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an