Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Integrable evolution equations on spaces of tensor densities and their
  peakon solutions   We study a family of equations defined on the space of tensor densities of
weight $\lambda$ on the circle and introduce two integrable PDE. One of the
equations turns out to be closely related to the inviscid Burgers equation
while the other has not been identified in any form before. We present their
Lax pair formulations and describe their bihamiltonian structures. We prove
local wellposedness of the corresponding Cauchy problem and include results on
blow-up as well as global existence of solutions. Moreover, we construct
"peakon" and "multi-peakon" solutions for all $\lambda \neq 0,1$, and
"shock-peakons" for $\lambda = 3$. We argue that there is a natural geometric
framework for these equations that includes other well-known integrable
equations and which is based on V. Arnold's approach to Euler equations on Lie
groups.

8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an