Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Partial differential systems with nonlocal nonlinearities: Generation
  and solutions   We develop a method for generating solutions to large classes of evolutionary
partial differential systems with nonlocal nonlinearities. For arbitrary
initial data, the solutions are generated from the corresponding linearized
equations. The key is a Fredholm integral equation relating the linearized flow
to an auxiliary linear flow. It is analogous to the Marchenko integral equation
in integrable systems. We show explicitly how this can be achieved through
several examples including reaction-diffusion systems with nonlocal quadratic
nonlinearities and the nonlinear Schrodinger equation with a nonlocal cubic
nonlinearity. In each case we demonstrate our approach with numerical
simulations. We discuss the effectiveness of our approach and how it might be
extended.

16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int