1,721,041 research outputs found
Hamiltonian dynamics
No full textThis is both a textbook and a monograph. It is partially based on a two-semester course, held by the author for third-year students in physics and mathematics at the University of Salerno, on analytical mechanics, differential geometry, symplectic manifolds and integrable systems. As a textbook, it provides a systematic and self-consistent formulation of Hamiltonian dynamics both in a rigorous coordinate language and in the modern language of differential geometry. It also presents powerful mathematical methods of theoretical physics, especially in gauge theories and general relativity. As a
Nambu Dynamics, n-Lie Algebras and Integrability (Edited by Ivaïlo Mladenov, Gaetano Vilasi and Akira Yoshioka, Softex, Sofia 2009)
No full textOn the Hamiltonian Structures of the Korteweg-de Vries and sine-Gordon Theories.
No full textWe construct a Miura-like transformation which transforms symplectic forms, Poisson brackets and conservation laws of KdV into those of SG, and then, transforms the hamiltonian flow of KdV into a one-parameter symmetry group of SG
An integrable model in general relativity
No full textIt is shown that gravitational fields invariant for a
non Abelian 2-dimensional Lie algebra of Killing fields are
parameterized either by solutions of a transcendental equation
(the tortoise equation) or by solutions of a linear second
order partial differential equation (the Laplace equation
or the Darboux equation) on the plane. Those determined
via Laplace or Darboux equations are exact nonlinear gravitational
waves obeying to two nonlinear superposition laws
GEOMETRY OF THE RECURSION OPERATORS FOR THE GMV SYSTEM
No full textWe consider the Recursion Operator approach to the soliton equations related to a auxiliary linear
system introduced recently by Gerdjikov, Mikhailov and Valchev (GMV system) and their interpretation
as dual of Nijenhuis tensors on the manifold of potentials
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