733 research outputs found

### Theoretical modeling of an A6 relativistic magnetron

The analytical modeling of the initialization stage of a relativistic magnetron of the A6 cylindrical design is presented, where only two dominant modes are used: a direct current (dc) background mode and a radio frequency (rf) pump mode. These two modes interaction nonlinearly, with the dc background being driven by the dc electromagnetic forces and the ponderomotive forces of the rf mode, while the rf mode is the most unstable linear eigenmode on this dc background. In cylindrical geometry, the diocotron resonance is found to occur over a broader region than in planar models. In fact, in certain parameter regimes, the resonance can appear twice, once near the Brillouin edge, and second, just below the anode. In these parameter regimes, the oscillating electrons can be accelerated twice. Numerical results for the initiation stage agree quite well with the known experimental results on the A6. Results for 350 kV are emphasized, and similar results have also been obtained for voltages between 300 and 500 kV. Numerical data are presented that indicate a possible source for a nonlinear instability, which could give rise to pulse shortening, in the later operating stage, where the device should be smoothly delivering power

### Integration of a generalized H\'enon-Heiles Hamiltonian

The generalized H\'enon-Heiles Hamiltonian
$H=1/2(P_X^2+P_Y^2+c_1X^2+c_2Y^2)+aXY^2-bX^3/3$ with an additional
nonpolynomial term $\mu Y^{-2}$ is known to be Liouville integrable for three
sets of values of $(b/a,c_1,c_2)$. It has been previously integrated by genus
two theta functions only in one of these cases. Defining the separating
variables of the Hamilton-Jacobi equations, we succeed here, in the two other
cases, to integrate the equations of motion with hyperelliptic functions.Comment: LaTex 2e. To appear, Journal of Mathematical Physic

### 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

### 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

### Unstaggered-staggered solitons in two-component discrete nonlinear Schr\"{o}dinger lattices

We present stable bright solitons built of coupled unstaggered and staggered
components in a symmetric system of two discrete nonlinear Schr\"{o}dinger
(DNLS) equations with the attractive self-phase-modulation (SPM) nonlinearity,
coupled by the repulsive cross-phase-modulation (XPM) interaction. These mixed
modes are of a "symbiotic" type, as each component in isolation may only carry
ordinary unstaggered solitons. The results are obtained in an analytical form,
using the variational and Thomas-Fermi approximations (VA and TFA), and the
generalized Vakhitov-Kolokolov (VK) criterion for the evaluation of the
stability. The analytical predictions are verified against numerical results.
Almost all the symbiotic solitons are predicted by the VA quite accurately, and
are stable. Close to a boundary of the existence region of the solitons (which
may feature several connected branches), there are broad solitons which are not
well approximated by the VA, and are unstable

### 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

### Quantized representation of some nonlinear integrable evolution equations on the soliton sector

The Hirota algorithm for solving several integrable nonlinear evolution
equations is suggestive of a simple quantized representation of these equations
and their soliton solutions over a Fock space of bosons or of fermions. The
classical nonlinear wave equation becomes a nonlinear equation for an operator.
The solution of this equation is constructed through the operator analog of the
Hirota transformation. The classical N-solitons solution is the expectation
value of the solution operator in an N-particle state in the Fock space.Comment: 12 page

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