Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Group analysis of differential equations and generalized functions   We present an extension of the methods of classical Lie group analysis of
differential equations to equations involving generalized functions (in
particular: distributions). A suitable framework for such a generalization is
provided by Colombeau's theory of algebras of generalized functions. We show
that under some mild conditions on the differential equations, symmetries of
classical solutions remain symmetries for generalized solutions. Moreover, we
introduce a generalization of the infinitesimal methods of group analysis that
allows to compute symmetries of linear and nonlinear differential equations
containing generalized function terms. Thereby, the group generators and group
actions may be given by generalized functions themselves.

10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg