Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-Standard Analysis, Multiplication of Schwartz Distributions and
  Delta-Like Solution of Hopf's Equation   We construct an algebra of generalized functions
$^*\mathcal{E}(\mathbb{R}^d)$. We also construct an embedding of the space of
Schwartz distributions $\mathcal{D}^\prime(\mathbb{R}^d)$ into
$^*\mathcal{E}(\mathbb{R}^d)$ and thus present a solution of the problem of
multiplication of Schwartz distributions which improves J.F. Colombeau's
solution. As an application we prove the existence of a weak delta-like
solution in ${^*\mathcal{E}(\mathbb{R}^d)}$ of the Hopf equation. This solution
does not have a counterpart in the classical theory of partial differential
equations. Our result improves a similar result by M. Radyna obtained in the
framework of perturbation theory.

7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an