1,199 research outputs found
Non-integrability of a fifth order equation with integrable two-body dynamics
We consider the fifth order partial differential equation (PDE) u4x,t?5uxxt+4ut+uu5x+2uxu4x?5uu3x?10uxuxx+12uux=0, which is a generalization of the integrable Camassa-Holm equation. The fifth order PDE has exact solutions in terms of an arbitrary number of superposed pulsons, with geodesic Hamiltonian dynamics that is known to be integrable in the two-body case N=2. Numerical simulations show that the pulsons are stable, dominate the initial value problem and scatter elastically. These characteristics are reminiscent of solitons in integrable systems. However, after demonstrating the non-existence of a suitable Lagrangian or bi-Hamiltonian structure, and obtaining negative results from Painlev\'{e} analysis and the Wahlquist-Estabrook method, we assert that the fifth order PDE is not integrable
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
Interwar Innovation in Three Navies: U.S. Navy, Royal Navy, Imperial Japanese Navy
In 1919, three major naval powers—Great Britain, Japan, and the United States—faced two major challenges: integrating new technology into their doctrines and organizations, and coping with reduced naval expenditures and arms treaties that came as a postwar reaction to armaments spending
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
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
Innovation in Carrier Aviation
This study is about innovations in carrier aviation and the spread of those innovations from one navy to the navy of a close ally. The innovations are the angled flight deck; the steam catapult; and the mirror and lighted landing aid that enabled pilots to land jet aircraft on a carrier’s short and narrow flight deck.https://digital-commons.usnwc.edu/usnwc-newport-papers/1036/thumbnail.jp
- …