Exact Solutions to the Beltrami Equation with a Non-constant $$\alpha({\bf x})$$Regular and Chaotic Dynamics - Tập 26 - Trang 692-699 - 2021
Oleg Bogoyavlenskij, Yuyang Peng
Infinite families of new exact solutions to the Beltrami equation with a
non-constant $$\alpha({\bf x})$$ are derived. Differential operators connecting
the steady axisymmetric Klein – Gordon equation and a special case of the Grad –
Shafranov equation are constructed. A Lie semi-group of nonlinear
transformations of the Grad – Shafranov equation is found.... hiện toàn bộ
Point vortices and polynomials of the Sawada-Kotera and Kaup-Kupershmidt equationsRegular and Chaotic Dynamics - Tập 16 - Trang 562-576 - 2011
Maria V. Demina, Nikolai A. Kudryashov
Rational solutions and special polynomials associated with the generalized K 2
hierarchy are studied. This hierarchy is related to the Sawada-Kotera and
Kaup-Kupershmidt equations and some other integrable partial differential
equations including the Fordy-Gibbons equation. Differential-difference
relations and differential equations satisfied by the polynomials are derived.
The relationship betwe... hiện toàn bộ
Poisson structures for geometric curve flows in semi-simple homogeneous spacesRegular and Chaotic Dynamics - Tập 15 - Trang 532-550 - 2010
G. Marí Beffa, P. J. Olver
We apply the equivariant method of moving frames to investigate the existence of
Poisson structures for geometric curve flows in semi-simple homogeneous spaces.
We derive explicit compatibility conditions that ensure that a geometric flow
induces a Hamiltonian evolution of the associated differential invariants. Our
results are illustrated by several examples of geometric interest.
The Lagrange-D’Alembert-Poincaré equations and integrability for the Euler’s diskRegular and Chaotic Dynamics - Tập 12 - Trang 56-67 - 2007
H. Cendra, V. A. Díaz
Nonholonomic systems are described by the Lagrange-D’Alembert’s principle. The
presence of symmetry leads, upon the choice of an arbitrary principal
connection, to a reduced D’Alembert’s principle and to the
Lagrange-D’Alembert-Poincaré reduced equations. The case of rolling constraints
has a long history and it has been the purpose of many works in recent times. In
this paper we find reduced equa... hiện toàn bộ
Dynamics of the finite-dimensional Kuramoto model: Global and cluster synchronizationRegular and Chaotic Dynamics - Tập 20 Số 1 - Trang 37-48 - 2015
Belykh, Vladimir N., Petrov, Valentin S., Osipov, Grigory V.
Synchronization phenomena in networks of globally coupled non-identical
oscillators have been one of the key problems in nonlinear dynamics over the
years. The main model used within this framework is the Kuramoto model. This
model shows three main types of behavior: global synchronization, cluster
synchronization including chimera states and totally incoherent behavior. We
present new sufficient ... hiện toàn bộ
The Centroid-Deformation Decomposition for Buoyant Vortex Patch MotionRegular and Chaotic Dynamics - Tập 26 - Trang 577-599 - 2021
Banavara N. Shashikanth, Rangachari Kidambi
The motion of a two-dimensional buoyant vortex patch, i. e., a vortex patch with
a uniform density different from the uniform density of the surrounding fluid,
is analyzed in terms of evolution equations for the motion of its centroid,
deformation of its boundary and the strength distribution of a vortex sheet
which is essential to enforce pressure continuity across the boundary. The
equations for... hiện toàn bộ
Normal forms, stability and splitting of invariant manifolds II. Finitely differentiable HamiltoniansRegular and Chaotic Dynamics - Tập 18 - Trang 261-276 - 2013
Abed Bounemoura
This paper is a sequel to “Normal forms, stability and splitting of invariant
manifolds I. Gevrey Hamiltonians”, in which we gave a new construction of
resonant normal forms with an exponentially small remainder for
near-integrableGevrey Hamiltonians at a quasiperiodic frequency, using a method
of periodic approximations. In this second part we focus on finitely
differentiable Hamiltonians, and we... hiện toàn bộ
On Periodic Poincaré Motions in the Case of Degeneracy of an Unperturbed SystemRegular and Chaotic Dynamics - Tập 25 - Trang 111-120 - 2020
Anatoly P. Markeev
This paper is concerned with a one-degree-of-freedom system close to an
integrable system. It is assumed that the Hamiltonian function of the system is
analytic in all its arguments, its perturbing part is periodic in time, and the
unperturbed Hamiltonian function is degenerate. The existence of periodic
motions with a period divisible by the period of perturbation is shown by the
Poincaré methods... hiện toàn bộ