497 research outputs found
A class of equations with peakon and pulson solutions (with an Appendix by Harry Braden and John Byatt-Smith)
We consider a family of integro-differential equations depending upon a
parameter as well as a symmetric integral kernel . When and
is the peakon kernel (i.e. up to rescaling) the
dispersionless Camassa-Holm equation results, while the Degasperis-Procesi
equation is obtained from the peakon kernel with . Although these two
cases are integrable, generically the corresponding integro-PDE is
non-integrable. However,for the family restricts to the pulson family of
Fringer & Holm, which is Hamiltonian and numerically displays elastic
scattering of pulses. On the other hand, for arbitrary it is still possible
to construct a nonlocal Hamiltonian structure provided that is the peakon
kernel or one of its degenerations: we present a proof of this fact using an
associated functional equation for the skew-symmetric antiderivative of .
The nonlocal bracket reduces to a non-canonical Poisson bracket for the peakon
dynamical system, for any value of .Comment: Contribution to volume of Journal of Nonlinear Mathematical Physics
in honour of Francesco Caloger
A lattice model of hydrophobic interactions
Hydrogen bonding is modeled in terms of virtual exchange of protons between
water molecules. A simple lattice model is analyzed, using ideas and techniques
from the theory of correlated electrons in metals. Reasonable parameters
reproduce observed magnitudes and temperature dependence of the hydrophobic
interaction between substitutional impurities and water within this lattice.Comment: 7 pages, 3 figures. To appear in Europhysics Letter
Inverse problems associated with integrable equations of Camassa-Holm type; explicit formulas on the real axis, I
The inverse problem which arises in the Camassa--Holm equation is revisited
for the class of discrete densities. The method of solution relies on the use
of orthogonal polynomials. The explicit formulas are obtained directly from the
analysis on the real axis without any additional transformation to a "string"
type boundary value problem known from prior works
Ac Stark Effects and Harmonic Generation in Periodic Potentials
The ac Stark effect can shift initially nonresonant minibands in
semiconductor superlattices into multiphoton resonances. This effect can result
in strongly enhanced generation of a particular desired harmonic of the driving
laser frequency, at isolated values of the amplitude.Comment: RevTeX, 10 pages (4 figures available on request), Preprint
UCSBTH-93-2
Path integral for a relativistic Aharonov-Bohm-Coulomb system
The path integral for the relativistic spinless Aharonov-Bohm-Coulomb system
is solved, and the energy spectra are extracted from the resulting amplitude.Comment: 6 pages, Revte
Unusually High Thermal Conductivity of Carbon Nanotubes
Combining equilibrium and non-equilibrium molecular dynamics simulations with
accurate carbon potentials, we determine the thermal conductivity of
carbon nanotubes and its dependence on temperature. Our results suggest an
unusually high value ~W/mK for an isolated
(10,10) nanotube at room temperature, comparable to the thermal conductivity of
a hypothetical isolated graphene monolayer or diamond. Our results suggest that
these high values of are associated with the large phonon mean free
paths in these systems; substantially lower values are predicted and observed
for the basal plane of bulk graphite.Comment: 4 pages 3 figures (5 postscript files), submitted for publicatio
Negative order KdV equation with both solitons and kink wave solutions
In this paper, we report an interesting integrable equation that has both
solitons and kink solutions. The integrable equation we study is
, which actually comes from the negative KdV
hierarchy and could be transformed to the Camassa-Holm equation through a gauge
transform. The Lax pair of the equation is derived to guarantee its
integrability, and furthermore the equation is shown to have classical
solitons, periodic soliton and kink solutions
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