Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the classification of conditionally integrable evolution systems in
  (1+1) dimensions   We generalize earlier results of Fokas and Liu and find all locally analytic
(1+1)-dimensional evolution equations of order $n$ that admit an $N$-shock type
solution with $N\leq n+1$.
  To this end we develop a refinement of the technique from our earlier work
(A. Sergyeyev, J. Phys. A: Math. Gen, 35 (2002), 7653--7660), where we
completely characterized all (1+1)-dimensional evolution systems
$\bi{u}_t=\bi{F}(x,t,\bi{u},\p\bi{u}/\p x,...,\p^n\bi{u}/\p x^n)$ that are
conditionally invariant under a given generalized (Lie--B\"acklund) vector
field $\bi{Q}(x,t,\bi{u},\p\bi{u}/\p x,...,\p^k\bi{u}/\p x^k)\p/\p\bi{u}$ under
the assumption that the system of ODEs $\bi{Q}=0$ is totally nondegenerate.
Every such conditionally invariant evolution system admits a reduction to a
system of ODEs in $t$, thus being a nonlinear counterpart to quasi-exactly
solvable models in quantum mechanics.
  Keywords: Exact solutions, nonlinear evolution equations, conditional
integrability, generalized symmetries, reduction, generalized conditional
symmetries
  MSC 2000: 35A30, 35G25, 81U15, 35N10, 37K35, 58J70, 58J72, 34A34

23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph