603 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
Bridge Hopping on Conducting Polymers in Solution
Configurational fluctuations of conducting polymers in solution can bring
into proximity monomers which are distant from each other along the backbone.
Electrons can hop between these monomers across the "bridges" so formed. We
show how this can lead to (i) a collapse transition for metallic polymers, and
(ii) to the observed dramatic efficiency of acceptor molecules for quenching
fluorescence in semiconducting polymers.Comment: RevTeX 12 pages + 2 Postscript figure
Two-component generalizations of the Camassa-Holm equation
A classification of integrable two-component systems of non-evolutionary partial differential equations that are analogous to the Camassa-Holm equation is carried out via the perturbative symmetry approach. Independently, a classification of compatible pairs of Hamiltonian operators is carried out, which leads to bi-Hamiltonian structures for the same systems of equations. Some exact solutions and Lax pairs are also constructed for the systems considered
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
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