7,436 research outputs found
A Characterization of Discrete Time Soliton Equations
We propose a method to characterize discrete time evolution equations, which
generalize discrete time soliton equations, including the -difference
Painlev\'e IV equations discussed recently by Kajiwara, Noumi and Yamada.Comment: 13 page
Disordered Regimes of the one-dimensional complex Ginzburg-Landau equation
I review recent work on the ``phase diagram'' of the one-dimensional complex
Ginzburg-Landau equation for system sizes at which chaos is extensive.
Particular attention is paid to a detailed description of the spatiotemporally
disordered regimes encountered. The nature of the transition lines separating
these phases is discussed, and preliminary results are presented which aim at
evaluating the phase diagram in the infinite-size, infinite-time, thermodynamic
limit.Comment: 14 pages, LaTeX, 9 figures available by anonymous ftp to
amoco.saclay.cea.fr in directory pub/chate, or by requesting them to
[email protected]
Completeness of the cubic and quartic H\'enon-Heiles Hamiltonians
The quartic H\'enon-Heiles Hamiltonian passes the Painlev\'e test for
only four sets of values of the constants. Only one of these, identical to the
traveling wave reduction of the Manakov system, has been explicitly integrated
(Wojciechowski, 1985), while the three others are not yet integrated in the
generic case . We integrate them by building
a birational transformation to two fourth order first degree equations in the
classification (Cosgrove, 2000) of such polynomial equations which possess the
Painlev\'e property. This transformation involves the stationary reduction of
various partial differential equations (PDEs). The result is the same as for
the three cubic H\'enon-Heiles Hamiltonians, namely, in all four quartic cases,
a general solution which is meromorphic and hyperelliptic with genus two. As a
consequence, no additional autonomous term can be added to either the cubic or
the quartic Hamiltonians without destroying the Painlev\'e integrability
(completeness property).Comment: 10 pages, To appear, Theor.Math.Phys. Gallipoli, 34 June--3 July 200
Zygomatic implant penetration to the central portion of orbit: a case report
Background: Zygomatic implants have been proposed in literature for atrophic maxillary fixed oral rehabilitations. The aim of the present research was to evaluate, by a clinical and tomography assessment, a surgical complication of a zygomatic implant penetration to the orbit. Case presentation: A 56 year-old female patient was visited for pain and swelling in the left orbit after a zygomatic implant protocol. The orbit invasion of the zygomatic implant screw was confirmed by the CBCT scan. The patient was treated for surgical implant removal and the peri- and post-operative symptoms were assessed. No neurological complications were reported at the follow-up. The ocular motility and the visual acuity were well maintained. No purulent secretion or inflammatory evidence were reported in the post-operative healing phases. Conclusion: The penetration of the orbit during a zygomatic implant positioning is a surgical complication that could compromise the sight and movements of the eye. In the present case report, a zygomatic implant removal resulted in an uneventful healing phase with recovery of the eye functions
Hyper-complex four-manifolds from the Tzitz\'eica equation
It is shown how solutions to the Tzitz\'eica equation can be used to
construct a family of (pseudo) hyper-complex metrics in four dimensions.Comment: To be published in J.Math.Phy
Metastable hydrogels from aromatic dipeptides
We demonstrate that the well-known self-assembling dipeptide diphenylalanine (FF) and its amidated derivative (FF-NH2) can form metastable hydrogels upon sonication of the dipeptide solutions. The hydrogels show instantaneous syneresis upon mechanical contact resulting in rapid expulsion of water and collapse into a semi-solid gel
The classification of all single travelling wave solutions to Calogero-Degasperis-Focas equation
Under the travelling wave transformation, Calogero-Degasperis-Focas equation
was reduced to an ordinary differential equation. Using a symmetry group of
one-parameter, this ODE was reduced to a second order linear inhomogeneous ODE.
Furthermore, we applied the change of the variable and complete discrimination
system for polynomial to solve the corresponding integrals and obtained the
classification of all single travelling wave solutions to
Calogero-Degasperis-Focas equation.Comment: 9 page
Multivortex Solutions of the Weierstrass Representation
The connection between the complex Sine and Sinh-Gordon equations on the
complex plane associated with a Weierstrass type system and the possibility of
construction of several classes of multivortex solutions is discussed in
detail. We perform the Painlev\'e test and analyse the possibility of deriving
the B\"acklund transformation from the singularity analysis of the complex
Sine-Gordon equation. We make use of the analysis using the known relations for
the Painlev\'{e} equations to construct explicit formulae in terms of the
Umemura polynomials which are -functions for rational solutions of the
third Painlev\'{e} equation. New classes of multivortex solutions of a
Weierstrass system are obtained through the use of this proposed procedure.
Some physical applications are mentioned in the area of the vortex Higgs
model when the complex Sine-Gordon equation is reduced to coupled Riccati
equations.Comment: 27 pages LaTeX2e, 1 encapsulated Postscript figur
Singularity confinement and algebraic integrability
Two important notions of integrability for discrete mappings are algebraic
integrability and singularity confinement, have been used for discrete
mappings. Algebraic integrability is related to the existence of sufficiently
many conserved quantities whereas singularity confinement is associated with
the local analysis of singularities. In this paper, the relationship between
these two notions is explored for birational autonomous mappings. Two types of
results are obtained: first, algebraically integrable mappings are shown to
have the singularity confinement property. Second, a proof of the non-existence
of algebraic conserved quantities of discrete systems based on the lack of
confinement property is given.Comment: 18 pages, no figur
Conditional symmetries and Riemann invariants for inhomogeneous hydrodynamic-type systems
A new approach to the solution of quasilinear nonelliptic first-order systems
of inhomogeneous PDEs in many dimensions is presented. It is based on a version
of the conditional symmetry and Riemann invariant methods. We discuss in detail
the necessary and sufficient conditions for the existence of rank-2 and rank-3
solutions expressible in terms of Riemann invariants. We perform the analysis
using the Cayley-Hamilton theorem for a certain algebraic system associated
with the initial system. The problem of finding such solutions has been reduced
to expanding a set of trace conditions on wave vectors and their profiles which
are expressible in terms of Riemann invariants. A couple of theorems useful for
the construction of such solutions are given. These theoretical considerations
are illustrated by the example of inhomogeneous equations of fluid dynamics
which describe motion of an ideal fluid subjected to gravitational and Coriolis
forces. Several new rank-2 solutions are obtained. Some physical interpretation
of these results is given.Comment: 19 page
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