Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Properties of Hamiltonian Structures for a Class of Evolutionary PDEs   In \cite{LZ2} it is proved that for certain class of perturbations of the
hyperbolic equation $u_t=f(u) u_x$, there exist changes of coordinate, called
quasi-Miura transformations, that reduce the perturbed equations to the
unperturbed one. We prove in the present paper that if in addition the
perturbed equations possess Hamiltonian structures of certain type, the same
quasi-Miura transformations also reduce the Hamiltonian structures to their
leading terms. By applying this result, we obtain a criterion of the existence
of Hamiltonian structures for a class of scalar evolutionary PDEs and an
algorithm to find out the Hamiltonian structures.

25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th