Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Modified KdV hierarchy : Lax pair representation and bi-Hamiltonian
  structure   We consider equations in the modified KdV (mKdV) hierarchy and make use of
the Miura transformation to construct expressions for their Lax pair. We derive
a Lagrangian-based approach to study the bi-Hamiltonian structure of the mKdV
equations. We also show that the complex modified KdV (cmKdV) equation follows
from the action principle to have a Lagrangian representation. This
representation not only provides a basis to write the cmKdV equation in the
canonical form endowed with an appropriate Poisson structure but also help us
construct a semianalytical solution of it. The solution obtained by us may
serve as a useful guide for purely numerical routines which are currently being
used to solve the cmKdV eqution.

1
The categories of this paper are: cs
19
The categories of this paper are: eess
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an