17 research outputs found
The Hamilton-Jacobi treatment for non-abelian Chern-Simons system
The non-abelian Chern-Simons field interacting with component complex
field is treated as a constrained system using the Hamilton-Jacobi approach.
The reduced phase space Hamiltonian density is obtained without introducing
Lagrange multipliers and with out any additional gauge fixing condition. The
quantization of this system is also discussed.Comment: 7 pages, Late
Fractional conservation laws in optimal control theory
Using the recent formulation of Noether's theorem for the problems of the
calculus of variations with fractional derivatives, the Lagrange multiplier
technique, and the fractional Euler-Lagrange equations, we prove a Noether-like
theorem to the more general context of the fractional optimal control. As a
corollary, it follows that in the fractional case the autonomous Hamiltonian
does not define anymore a conservation law. Instead, it is proved that the
fractional conservation law adds to the Hamiltonian a new term which depends on
the fractional-order of differentiation, the generalized momentum, and the
fractional derivative of the state variable.Comment: The original publication is available at http://www.springerlink.com
Nonlinear Dynamic
Fractional Hamilton formalism within Caputo's derivative
In this paper we develop a fractional Hamiltonian formulation for dynamic
systems defined in terms of fractional Caputo derivatives. Expressions for
fractional canonical momenta and fractional canonical Hamiltonian are given,
and a set of fractional Hamiltonian equations are obtained. Using an example,
it is shown that the canonical fractional Hamiltonian and the fractional
Euler-Lagrange formulations lead to the same set of equations.Comment: 8 page
Cosmological perturbations in FRW model with scalar field within Hamilton-Jacobi formalism and symplectic projector method
The Hamilton-Jacobi analysis is applied to the dynamics of the scalar
fluctuations about the Friedmann-Robertson-Walker (FRW). The gauge conditions
are found from the consistency conditions. The physical degrees of freedom of
the model are obtain by symplectic projector method. The role of the linearly
dependent Hamiltonians and the gauge variables in Hamilton-Jacobi formalism is
discussed.Comment: 11 page
Time-Fractional KdV Equation: Formulation and Solution using Variational Methods
In this work, the semi-inverse method has been used to derive the Lagrangian
of the Korteweg-de Vries (KdV) equation. Then, the time operator of the
Lagrangian of the KdV equation has been transformed into fractional domain in
terms of the left-Riemann-Liouville fractional differential operator. The
variational of the functional of this Lagrangian leads neatly to Euler-Lagrange
equation. Via Agrawal's method, one can easily derive the time-fractional KdV
equation from this Euler-Lagrange equation. Remarkably, the time-fractional
term in the resulting KdV equation is obtained in Riesz fractional derivative
in a direct manner. As a second step, the derived time-fractional KdV equation
is solved using He's variational-iteration method. The calculations are carried
out using initial condition depends on the nonlinear and dispersion
coefficients of the KdV equation. We remark that more pronounced effects and
deeper insight into the formation and properties of the resulting solitary wave
by additionally considering the fractional order derivative beside the
nonlinearity and dispersion terms.Comment: The paper has been rewritten, 12 pages, 3 figure
Fractional Dynamics of Relativistic Particle
Fractional dynamics of relativistic particle is discussed. Derivatives of
fractional orders with respect to proper time describe long-term memory effects
that correspond to intrinsic dissipative processes. Relativistic particle
subjected to a non-potential four-force is considered as a nonholonomic system.
The nonholonomic constraint in four-dimensional space-time represents the
relativistic invariance by the equation for four-velocity u_{\mu}
u^{\mu}+c^2=0, where c is a speed of light in vacuum. In the general case, the
fractional dynamics of relativistic particle is described as non-Hamiltonian
and dissipative. Conditions for fractional relativistic particle to be a
Hamiltonian system are considered