Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Classification of Integrable Evolution Equations of the Form
  $u_t=u_{xxx}+f(t,x,u,u_x,u_{xx})$   We obtain the classification of integrable equations of the form
$u_t=u_{xxx}+f(t,x,u,u_x,u_{xx})$ using the formal symmetry method of Mikhailov
et al [A.V.Mikhailov, A.B.Shabat and V.V.Sokolov, in {\it What is
Integrability} edited by V.E. Zakharov (Springer-Verlag, Berlin 1991)]. We show
that all such equations can be transformed to an integrable equation of the
form $v_t=v_{xxx}+f(v,v_x,v_{xx})$ using transformations
$\Phi(x,t,u,v,u_x,v_x)=0$, and the $u_{xx}$ dependence can be eliminated except
for two equations.

17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
2
The categories of this paper are: math
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con