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In this paper we study an incompressible inviscid fluid when the initial vorticity is sharply concentrated in N disjoint regions. This problem has been well studied when a planar symmetry is present, i.e., the fluid moves in R 2 . R 2 . In this case we know that, when the diameter σ of each...
Three new exact periodic solutions of the complex Ginzburg–Landau equation are obtained in terms of the Weierstrass elliptic function ℘. Furthermore, the new periodic solutions and other shock solutions appear as their bounded limits (along the real axis) for particular relationships between...
A quantum algebra invariant integrable closed spin 1 chain is introduced and analyzed in detail. The Bethe ansatz equations as well as the energy eigenvalues of the model are obtained. The highest weight property of the Bethe vectors with respect to U q ( s l (2)) U q ( s l ( 2 ) ) is proved. ©...
We introduce a proposal to modify Einstein’s equations by embedding them in a larger symmetric hyperbolic system. The additional dynamical variables of the modified system are essentially first integrals of the original constraints. The extended system of equations reproduces the usual dynamics...
We present a mathematical framework of gauge theories that is based upon a skew-adjoint Lie algebra and a generalized Dirac operator, both acting on a Hilbert space. © 1999 American Institute of Physics.
Two supersymmetric classical mechanical systems are discussed. Concrete realizations are obtained by supposing that the dynamical variables take values in the Grassmann algebra B 2 B 2 with two generators. The equations of motion are explicitly solved, and the action of the supergroup on the...
Multidimensional gravity interacting with intersecting electric and magnetic p -branes is considered for fields depending on a single variable. Some general features of the system behavior are revealed without solving the field equations. Thus, essential asymptotic properties of isotropic...
It is outlined how deformations of field theoretical rigid symmetries can be constructed and classified by cohomological means in the extended antifield formalism. Special attention is devoted to deformations referring only to a subset of the rigid symmetries of a given model and leading to a...
We construct a general approach to the decomposition of the tangent bundle of pseudo-Riemannian manifolds into direct sums of subbundles, and the associated decomposition of geometric objects. An invariant structure H r H r defined as a set of r projection operators is used to induce...
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