12 research outputs found
Exact accelerating solitons in nonholonomic deformation of the KdV equation with two-fold integrable hierarchy
Recently proposed nonholonomic deformation of the KdV equation is solved
through inverse scattering method by constructing AKNS-type Lax pair. Exact and
explicit N-soliton solutions are found for the basic field and the deforming
function showing an unusual accelerated (decelerated) motion. A two-fold
integrable hierarchy is revealed, one with usual higher order dispersion and
the other with novel higher nonholonomic deformations.Comment: 7 pages, 2 figures, latex. Exact explicit exact N-soliton solutions
(through ISM) for KdV field u and deforming function w are included. Version
to be published in J. Phys.
On Non-Commutative Integrable Burgers Equations
We construct the recursion operators for the non-commutative Burgers
equations using their Lax operators. We investigate the existence of any
integrable mixed version of left- and right-handed Burgers equations on higher
symmetry grounds.Comment: 8 page
Negative Even Grade mKdV Hierarchy and its Soliton Solutions
In this paper we provide an algebraic construction for the negative even mKdV
hierarchy which gives rise to time evolutions associated to even graded Lie
algebraic structure. We propose a modification of the dressing method, in order
to incorporate a non-trivial vacuum configuration and construct a deformed
vertex operator for , that enable us to obtain explicit and
systematic solutions for the whole negative even grade equations
Recursion operator for stationary Nizhnik--Veselov--Novikov equation
We present a new general construction of recursion operator from zero
curvature representation. Using it, we find a recursion operator for the
stationary Nizhnik--Veselov--Novikov equation and present a few low order
symmetries generated with the help of this operator.Comment: 6 pages, LaTeX 2