53 research outputs found
Recursion Operators of Some Equations of Hydrodynamic Type
We give a general method for constructing recursion operators for some
equations of hydrodynamic type, admitting a nonstandard Lax representation. We
give several examples for N=2 and N=3 containing the equations of shallow water
waves and its generalizations with their first two higher symmetries and their
recursion operators. We also discuss a reduction of systems to
systems of some new equations of hydrodynamic type.Comment: Latex File (amssymb), 22 page
U(1)-invariant membranes: the geometric formulation, Abel and pendulum differential equations
The geometric approach to study the dynamics of U(1)-invariant membranes is
developed. The approach reveals an important role of the Abel nonlinear
differential equation of the first type with variable coefficients depending on
time and one of the membrane extendedness parameters. The general solution of
the Abel equation is constructed. Exact solutions of the whole system of
membrane equations in the D=5 Minkowski space-time are found and classified. It
is shown that if the radial component of the membrane world vector is only time
dependent then the dynamics is described by the pendulum equation.Comment: 19 pages, v3 published versio
Hamiltonian of Tensionless Strings with Tensor Central Charge Coordinates
A new class of twistor-like string models in four-dimensional space-time
extended by the addition of six tensorial central charge (TCC) coordinates
is studied. The Hamiltonian of tensionless string in the extended
space-time is derived and its symmetries are investigated. We establish that
the string constraints reduce the number of independent TCC coordinates
to one real effective coordinate which composes an effective
5-dimensional target space together with the coordinates. We construct
the P.B. algebra of the first class constraints and discover that it coincides
with the P.B. algebra of tensionless strings. The Lorentz covariant
antisymmetric Dirac -matrix of the P.B. of the second class
constraints is constructed and its algebraic structure is further presented.Comment: 18 pages, Latex, no figure
Tensionless String in the Notoph Background
We study the interaction between a tensionless (null) string and an
antisymmetric background field B_{ab} using a 2-component spinor formalism. A
geometric condition for the absence of such an interaction is formulated. We
show that only one gauge-invariant degree of freedom of the field B_{ab} does
not satisfy this condition. Identification of this degree of freedom with the
notoph field \phi of Ogievetskii-Polubarinov-Kalb-Ramond is suggested.
Application of a two-component spinor formalism allows us a reduction of the
complete system of non-linear partial differential equations and constraints
governing the interacting null string dynamics to a system of linear
differential equations for the basis spinors of the spin-frame. We find that
total effect of the interaction is contained in a single derivation coefficient
which is identified with the notoph field.Comment: 15 pages, no figures, RevTeX 3.
Tensionless strings: physical Fock space and higher spin fields
I study the physical Fock space of the tensionless string theory with
perimeter action, exploring its new gauge symmetry algebra. The cancellation of
conformal anomaly requires the space-time to be 13-dimensional. All particles
are massless and there are no tachyon states in the spectrum. The zero mode
conformal operator defines the levels of the physical Fock space. All levels
can be classified by the highest Casimir operator W of the little group E(11)
for massless particles in 11-dimensions. The ground state is infinitely
degenerated and contains massless gauge fields of arbitrary large integer spin,
realizing the irreducible representations of E(11) of fixed helicity. The
excitation levels realize CSR representations of little group E(11) with an
infinite number of helicities. After inspection of the first excitation level,
which, as I prove, is a physical null state, I conjecture that all excitation
levels are physical null states. In this theory the tensor field of the second
rank does not play any distinctive role and therefore one can suggest that in
this model there is no gravity.Comment: 22 pages, Latex, references adde
Integrable nonlinear equations on a circle
The concept of integrable boundary value problems for soliton equations on
and is extended to bounded regions enclosed by
smooth curves. Classes of integrable boundary conditions on a circle for the
Toda lattice and its reductions are found.Comment: 23 page
Hamiltonian structure and noncommutativity in -brane models with exotic supersymmetry
The Hamiltonian of the simplest super -brane model preserving 3/4 of the
D=4 N=1 supersymmetry in the centrally extended symplectic superspace is
derived and its symmetries are described. The constraints of the model are
covariantly separated into the first- and the second-class sets and the Dirac
brackets (D.B.) are constructed. We show the D.B. noncommutativity of the super
-brane coordinates and find the D.B. realization of the
superalgebra. Established is the coincidence of the D.B. and Poisson bracket
realizations of the superalgebra on the constraint surface and the
absence there of anomaly terms in the commutation relations for the quantized
generators of the superalgebra.Comment: Latex, 27 pages, no figures. Latex packages amsfonts and euscript are
use
Hydrodynamic type integrable equations on a segment and a half-line
The concept of integrable boundary conditions is applied to hydrodynamic type
systems. Examples of such boundary conditions for dispersionless Toda systems
are obtained. The close relation of integrable boundary conditions with
integrable reductions of multi-field systems is observed. The problem of
consistency of boundary conditions with the Hamiltonian formulation is
discussed. Examples of Hamiltonian integrable hydrodynamic type systems on a
segment and a semi-line are presented
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