Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Emerging problems in approximation theory for the numerical solution of
  nonlinear PDEs of integrable type   In this paper we present some open problems pertaining to the approximation
theory involved in the solution of the important class of Nonlinear Partial
Differential Equations (NPDEs) of integrable type. For this class of NPDEs, any
Initial Value Problem (IVP) can be theoretically solved by the Inverse
Scattering Transform (IST) technique whose main steps involve the solution of
Volterra equations with structured kernels on unbounded domains, the solution
of Fredholm integral equations and the identification of coefficients and
parameters of monomial-exponential sums. The aim of this paper is twofold:
propose a method for solving the above mentioned problems under particular
hypothesis and arouse interest in these problems in order to develop an
effective method which works under more general assumptions.

22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex