Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A simple and direct method for generating travelling wave solutions for
  nonlinear equations   We propose a simple and direct method for generating travelling wave
solutions for nonlinear integrable equations. We illustrate how nontrivial
solutions for the KdV, the mKdV and the Boussinesq equations can be obtained
from simple solutions of linear equations. We describe how using this method, a
soliton solution of the KdV equation can yield soliton solutions for the mKdV
as well as the Boussinesq equations. Similarly, starting with cnoidal solutions
of the KdV equation, we can obtain the corresponding solutions for the mKdV as
well as the Boussinesq equations. Simple solutions of linear equations can also
lead to cnoidal solutions of nonlinear systems. Finally, we propose and solve
some new families of KdV equations and show how soliton solutions are also
obtained for the higher order equations of the KdV hierarchy using this method.

35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph