480 research outputs found
Rational Approximate Symmetries of KdV Equation
We construct one-parameter deformation of the Dorfman Hamiltonian operator
for the Riemann hierarchy using the quasi-Miura transformation from topological
field theory. In this way, one can get the approximately rational symmetries of
KdV equation and then investigate its bi-Hamiltonian structure.Comment: 14 pages, no figure
On a Order Reduction Theorem in the Lagrangian Formalism
We provide a new proof of a important theorem in the Lagrangian formalism
about necessary and sufficient conditions for a second-order variational system
of equations to follow from a first-order Lagrangian.Comment: 9 pages, LATEX, no figures; appear in Il Nuovo Cimento
On bi-Hamiltonian deformations of exact pencils of hydrodynamic type
In this paper we are interested in non trivial bi-Hamiltonian deformations of
the Poisson pencil \omega_{\lambda}=\omega_2+\lambda
\omega_1=u\delta'(x-y)+\f{1}{2}u_x\delta(x-y)+\lambda\delta'(x-y).
Deformations are generated by a sequence of vector fields ,
where each is homogenous of degree with respect to a grading
induced by rescaling. Constructing recursively the vector fields one
obtains two types of relations involving their unknown coefficients: one set of
linear relations and an other one which involves quadratic relations. We prove
that the set of linear relations has a geometric meaning: using
Miura-quasitriviality the set of linear relations expresses the tangency of the
vector fields to the symplectic leaves of and this tangency
condition is equivalent to the exactness of the pencil .
Moreover, extending the results of [17], we construct the non trivial
deformations of the Poisson pencil , up to the eighth order
in the deformation parameter, showing therefore that deformations are
unobstructed and that both Poisson structures are polynomial in the derivatives
of up to that order.Comment: 34 pages, revised version. Proof of Theorem 16 completely rewritten
due to an error in the first versio
Analytic structure of radiation boundary kernels for blackhole perturbations
Exact outer boundary conditions for gravitational perturbations of the
Schwarzschild metric feature integral convolution between a time-domain
boundary kernel and each radiative mode of the perturbation. For both axial
(Regge-Wheeler) and polar (Zerilli) perturbations, we study the Laplace
transform of such kernels as an analytic function of (dimensionless) Laplace
frequency. We present numerical evidence indicating that each such
frequency-domain boundary kernel admits a "sum-of-poles" representation. Our
work has been inspired by Alpert, Greengard, and Hagstrom's analysis of
nonreflecting boundary conditions for the ordinary scalar wave equation.Comment: revtex4, 14 pages, 12 figures, 3 table
Lie symmetries and solitons in nonlinear systems with spatially inhomogeneous nonlinearities
Using Lie group theory and canonical transformations we construct explicit
solutions of nonlinear Schrodinger equations with spatially inhomogeneous
nonlinearities. We present the general theory, use it to show that localized
nonlinearities can support bound states with an arbitrary number solitons and
discuss other applications of interest to the field of nonlinear matter waves
The Moyal bracket and the dispersionless limit of the KP hierarchy
A new Lax equation is introduced for the KP hierarchy which avoids the use of
pseudo-differential operators, as used in the Sato approach. This Lax equation
is closer to that used in the study of the dispersionless KP hierarchy, and is
obtained by replacing the Poisson bracket with the Moyal bracket. The
dispersionless limit, underwhich the Moyal bracket collapses to the Poisson
bracket, is particularly simple.Comment: 9 pages, LaTe
Involutive orbits of non-Noether symmetry groups
We consider set of functions on Poisson manifold related by continues
one-parameter group of transformations. Class of vector fields that produce
involutive families of functions is investigated and relationship between these
vector fields and non-Noether symmetries of Hamiltonian dynamical systems is
outlined. Theory is illustrated with sample models: modified Boussinesq system
and Broer-Kaup system.Comment: LaTeX 2e, 10 pages, no figure
The general dielectric tensor for bi-kappa magnetized plasmas
In this paper we derive the dielectric tensor for a plasma containing
particles described by an anisotropic superthermal (bi-kappa) velocity
distribution function. The tensor components are written in terms of the
two-variables kappa plasma special functions, recently defined by Gaelzer and
Ziebell [Phys. Plasmas 23, 022110 (2016)]. We also obtain various new
mathematical properties for these functions, which are useful for the
analytical treatment, numerical implementation and evaluation of the functions
and, consequently, of the dielectric tensor. The formalism developed here and
in the previous paper provides a mathematical framework for the study of
electromagnetic waves propagating at arbitrary angles and polarizations in a
superthermal plasma.Comment: Accepted for publication in Physics of Plasma
Conserved current for the Cotton tensor, black hole entropy and equivariant Pontryagin forms
The Chern-Simons lagrangian density in the space of metrics of a
3-dimensional manifold M is not invariant under the action of diffeomorphisms
on M. However, its Euler-Lagrange operator can be identified with the Cotton
tensor, which is invariant under diffeomorphims. As the lagrangian is not
invariant, Noether Theorem cannot be applied to obtain conserved currents. We
show that it is possible to obtain an equivariant conserved current for the
Cotton tensor by using the first equivariant Pontryagin form on the bundle of
metrics. Finally we define a hamiltonian current which gives the contribution
of the Chern-Simons term to the black hole entropy, energy and angular
momentum.Comment: 13 page
Complete integrability of derivative nonlinear Schr\"{o}dinger-type equations
We study matrix generalizations of derivative nonlinear Schr\"{o}dinger-type
equations, which were shown by Olver and Sokolov to possess a higher symmetry.
We prove that two of them are `C-integrable' and the rest of them are
`S-integrable' in Calogero's terminology.Comment: 14 pages, LaTeX2e (IOP style), to appear in Inverse Problem
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