72 research outputs found
Integrable relativistic systems given by Hamiltonians with momentum-spin-orbit coupling
In the paper we investigate the evolution of the relativistic particle
(massive and massless) with spin defined by Hamiltonian containing the terms
with momentum-spin-orbit coupling. We integrate the corresponding Hamiltonian
equations in quadratures and express their solutions in terms of elliptic
functions.Comment: 18 page
Weak Poisson structures on infinite dimensional manifolds and hamiltonian actions
We introduce a notion of a weak Poisson structure on a manifold modeled
on a locally convex space. This is done by specifying a Poisson bracket on a
subalgebra \cA \subeq C^\infty(M) which has to satisfy a non-degeneracy
condition (the differentials of elements of \cA separate tangent vectors) and
we postulate the existence of smooth Hamiltonian vector fields. Motivated by
applications to Hamiltonian actions, we focus on affine Poisson spaces which
include in particular the linear and affine Poisson structures on duals of
locally convex Lie algebras. As an interesting byproduct of our approach, we
can associate to an invariant symmetric bilinear form on a Lie algebra
\g and a -skew-symmetric derivation a weak affine Poisson
structure on \g itself. This leads naturally to a concept of a Hamiltonian
-action on a weak Poisson manifold with a \g-valued momentum map and hence
to a generalization of quasi-hamiltonian group actions
Hierarchy of integrable Hamiltonians describing of nonlinear n-wave interaction
In the paper we construct an hierarchy of integrable Hamiltonian systems
which describe the variation of n-wave envelopes in nonlinear dielectric
medium. The exact solutions for some special Hamiltonians are given in terms of
elliptic functions of the first kind.Comment: 17 page
Path space forms and surface holonomy
We develop parallel transport on path spaces from a differential geometric
approach, whose integral version connects with the category theoretic approach.
In the framework of 2-connections, our approach leads to further development of
higher gauge theory, where end points of the path need not be fixed.Comment: 6 pages, 2 figures. Talk delivered by S. Chatterjee at XXVIII WGMP,
28th June-4th July, 2009. Bialowieza, Polan
On the existence of optimal consensus control for the fractional Cucker–Smale model
This paper addresses the nonlinear Cucker–Smale optimal control problem under the interplay of memory effect. The aforementioned effect is included by employing the Caputo fractional
derivative in the equation representing the velocity of agents. Sufficient conditions for the existence of solutions to the considered problem are proved and the analysis of some particular
problems is illustrated by two numerical examples.publishe
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