Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Integrable peakon equations with cubic nonlinearity   We present a new integrable partial differential equation found by Vladimir
Novikov. Like the Camassa-Holm and Degasperis-Procesi equations, this new
equation admits peaked soliton (peakon) solutions, but it has nonlinear terms
that are cubic, rather than quadratic. We give a matrix Lax pair for V.
Novikov's equation, and show how it is related by a reciprocal transformation
to a negative flow in the Sawada-Kotera hierarchy. Infinitely many conserved
quantities are found, as well as a bi-Hamiltonian structure. The latter is used
to obtain the Hamiltonian form of the finite-dimensional system for the
interaction of $N$ peakons, and the two-body dynamics (N=2) is explicitly
integrated. Finally, all of this is compared with some analogous results for
another cubic peakon equation derived by Zhijun Qiao.

2
The categories of this paper are: math
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc