Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Integrable system with peakon, weak kink, and kink-peakon interactional
  solutions   In this paper, we study an integrable system with both quadratic and cubic
nonlinearity: $m_t=bu_x+1/2k_1[m(u^2-u^2_x)]_x+1/2k_2(2m u_x+m_xu)$,
$m=u-u_{xx}$, where $b$, $k_1$ and $k_2$ are arbitrary constants. This model is
kind of a cubic generalization of the Camassa-Holm (CH) equation:
$m_t+m_xu+2mu_x=0$. The equation is shown integrable with its Lax pair,
bi-Hamiltonian structure, and infinitely many conservation laws. In the case of
$b=0$, the peaked soliton (peakon) and multi-peakon solutions are studied. In
particular, the two-peakon dynamical system is explicitly presented and their
collisions are investigated in details. In the case of $b\neq0$ and $k_2=0$,
the weak kink and kink-peakon interactional solutions are found. Significant
difference from the CH equation is analyzed through a comparison. In the paper,
we also study all possible smooth one-soliton solutions for the system.

17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat