Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A numerical dressing method for the nonlinear superposition of solutions
  of the KdV equation   In this paper we present the unification of two existing numerical methods
for the construction of solutions of the Korteweg-de Vries (KdV) equation. The
first method is used to solve the Cauchy initial-value problem on the line for
rapidly decaying initial data. The second method is used to compute
finite-genus solutions of the KdV equation. The combination of these numerical
methods allows for the computation of exact solutions that are asymptotically
(quasi-)periodic finite-gap solutions and are a nonlinear superposition of
dispersive, soliton and (quasi-)periodic solutions in the finite (x,t)-plane.
Such solutions are referred to as superposition solutions. We compute these
solutions accurately for all values of x and t.

15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th