4,020 research outputs found
Variational derivation of the Camassa-Holm shallow water equation
We describe the physical hypothesis in which an approximate model of water
waves is obtained. For an irrotational unidirectional shallow water flow, we
derive the Camassa-Holm equation by a variational approach in the Lagrangian
formalism.Comment: 10 page
Geodesic Flow on the Diffeomorphism Group of the circle
We show that certain right-invariant metrics endow the infinite-dimensional
Lie group of all smooth orientation-preserving diffeomorphisms of the circle
with a Riemannian structure. The study of the Riemannian exponential map allows
us to prove infinite-dimensional counterparts of results from classical
Riemannian geometry: the Riemannian exponential map is a smooth local
diffeomorphism and the length-minimizing property of the geodesics holds.Comment: 15 page
On periodic water waves with Coriolis effects and isobaric streamlines
In this paper we prove that solutions of the f-plane approximation for
equatorial geophysical deep water waves, which have the property that the
pressure is constant along the streamlines and do not possess stagnation
points,are Gerstner-type waves. Furthermore, for waves traveling over a flat
bed, we prove that there are only laminar flow solutions with these properties.Comment: To appear in Journal of Nonlinear Mathematical Physics; 15 page
(8,0) Quantum mechanics and symmetry enhancement in type I' superstrings
The low-energy supersymmetric quantum mechanics describing D-particles in the
background of D8-branes and orientifold planes is analyzed in detail, including
a careful discussion of Gauss' law and normal ordering of operators. This
elucidates the mechanism that binds D-particles to an orientifold plane, in
accordance with the predictions of heterotic/type I duality. The ocurrence of
enhanced symmetries associated with massless bound states of a D-particle with
one orientifold plane is illustrated by the enhancement of
to and to at strong type I' coupling.
Enhancement to higher-rank groups involves both orientifold planes. For
example, the enhanced symmetry at the self-dual
radius of the heterotic string is seen as the result of two D8-branes
coinciding midway between the orientifold planes, while the enhanced
symmetry results from the coincidence of all sixteen D8-branes and
when they also coincide with an orientifold plane. As a separate by-product,
the s-rule of brane-engineered gauge theories is derived by relating it through
a chain of dualities to the Pauli exclusion principle.Comment: 30 pages LaTeX, Five figures. Two references added as well as some
Comments in section4. v4: Missing backslashes added to four reference
citations
Anomalous Creation of Branes
In certain circumstances when two branes pass through each other a third
brane is produced stretching between them. We explain this phenomenon by the
use of chains of dualities and the inflow of charge that is required for the
absence of chiral gauge anomalies when pairs of D-branes intersect.Comment: 7 pages, two figure
On the Cauchy problem for a nonlinearly dispersive wave equation
We establish the local well-posedness for a new nonlinearly dispersive wave
equation and we show that the equation has solutions that exist for indefinite
times as well as solutions which blowup in finite times. Furthermore, we derive
an explosion criterion for the equation and we give a sharp estimate from below
for the existence time of solutions with smooth initial data.Comment: arxiv version is already officia
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