487 research outputs found
On complete integrability of the Mikhailov-Novikov-Wang system
We obtain compatible Hamiltonian and symplectic structure for a new
two-component fifth-order integrable system recently found by Mikhailov,
Novikov and Wang (arXiv:0712.1972), and show that this system possesses a
hereditary recursion operator and infinitely many commuting symmetries and
conservation laws, as well as infinitely many compatible Hamiltonian and
symplectic structures, and is therefore completely integrable. The system in
question admits a reduction to the Kaup--Kupershmidt equation.Comment: 5 pages, no figure
Solitons created by chirped initial profiles in coherent pulse propagation
"Solitons created by chirped initial profiles in coherent pulse propagation", L.V.Hmurcik and
D.J.Kaup, Journal of the Optical Society of America, vol 69, p 597 (1979).If an incident pulse is chirped, the critical parameters for self-induced transparency to occur in coherent pulse propagation can no longer be obtained from the well-known McCall-Hahn area theorem. We have been able to obtain these parameters by solving the Zakharov-Shabat eigenvalue equation for the bound-state eigenvalues. We find that critical (threshold) areas will be increased for a chirped incident pulse in almost all cases, except for a box profile or for a pulse that is approximately box-like in shape. In these latter cases, the chirped critical areas will instead decrease for the second and all higher branches. The first branch’s critical area is always increased due to chirping
Quantum shock waves in the Heisenberg XY model
We show the existence of quantum states of the Heisenberg XY chain which
closely follow the motion of the corresponding semi-classical ones, and whose
evolution resemble the propagation of a shock wave in a fluid. These states are
exact solutions of the Schroedinger equation of the XY model and their
classical counterpart are simply domain walls or soliton-like solutions.Comment: 15 pages,6 figure
On the (Non)-Integrability of KdV Hierarchy with Self-consistent Sources
Non-holonomic deformations of integrable equations of the KdV hierarchy are
studied by using the expansions over the so-called "squared solutions" (squared
eigenfunctions). Such deformations are equivalent to perturbed models with
external (self-consistent) sources. In this regard, the KdV6 equation is viewed
as a special perturbation of KdV equation. Applying expansions over the
symplectic basis of squared eigenfunctions, the integrability properties of the
KdV hierarchy with generic self-consistent sources are analyzed. This allows
one to formulate a set of conditions on the perturbation terms that preserve
the integrability. The perturbation corrections to the scattering data and to
the corresponding action-angle variables are studied. The analysis shows that
although many nontrivial solutions of KdV equations with generic
self-consistent sources can be obtained by the Inverse Scattering Transform
(IST), there are solutions that, in principle, can not be obtained via IST.
Examples are considered showing the complete integrability of KdV6 with
perturbations that preserve the eigenvalues time-independent. In another type
of examples the soliton solutions of the perturbed equations are presented
where the perturbed eigenvalue depends explicitly on time. Such equations,
however in general, are not completely integrable.Comment: 16 pages, no figures, LaTe
The Davey Stewartson system and the B\"{a}cklund Transformations
We consider the (coupled) Davey-Stewartson (DS) system and its B\"{a}cklund
transformations (BT). Relations among the DS system, the double
Kadomtsev-Petviashvili (KP) system and the Ablowitz-Ladik hierarchy (ALH) are
established. The DS hierarchy and the double KP system are equivalent. The ALH
is the BT of the DS system in a certain reduction. {From} the BT of coupled DS
system we can obtain new coupled derivative nonlinear Schr\"{o}dinger
equations.Comment: 13 pages, LaTe
One-Dimensional Integrable Spinor BECs Mapped to Matrix Nonlinear Schr\"odinger Equation and Solution of Bogoliubov Equation in These Systems
In this short note, we construct mappings from one-dimensional integrable
spinor BECs to matrix nonlinear Schr\"odinger equation, and solve the
Bogoliubov equation of these systems. A map of spin- BEC is constructed from
the -dimensional spinor representation of irreducible tensor operators of
. Solutions of Bogoliubov equation are obtained with the aid of the
theory of squared Jost functions.Comment: 2.1 pages, JPSJ shortnote style. Published version. Note and
reference adde
Renormalization Group Theory for a Perturbed KdV Equation
We show that renormalization group(RG) theory can be used to give an analytic
description of the evolution of a perturbed KdV equation. The equations
describing the deformation of its shape as the effect of perturbation are RG
equations. The RG approach may be simpler than inverse scattering theory(IST)
and another approaches, because it dose not rely on any knowledge of IST and it
is very concise and easy to understand. To the best of our knowledge, this is
the first time that RG has been used in this way for the perturbed soliton
dynamics.Comment: 4 pages, no figure, revte
Zero curvature representation for a new fifth-order integrable system
In this brief note we present a zero-curvature representation for one of the
new integrable system found by Mikhailov, Novikov and Wang in nlin.SI/0601046.Comment: 2 pages, LaTeX 2e, no figure
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