Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Factorization method for nonlinear evolution equations Factorization
  method for nonlinear evolution equations   The traditional method of factorization can be used to obtain only the
particular solutions of the Li\'enard type ordinary differential equations. We
suggest a modification of the approach that can be used to construct general
solutions . We first demonstrate the effectiveness of our method by dealing
with a solvable form of the modified Emden-type equation and subsequently
employ it to obtain the solitary wave solutions of the KdV, mKdV, Rosenau-Hyman
(RH) and NLS equations. The solution of the mKdV equation, via the so-called
Muira transform, leads to a singular solution of the KdV equation in addition
to the well-known soliton solution supported by it. We obtain the solution of
the non-integrable RH equation in terms of the Jacobi function and show that,
although robust, it is structurally different from the KdV soliton. We also
find the soliton solution of the NLS equation that accounts for the evolution
of complex envelopes in an optical medium.

35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom