Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userOrder reductions of Lorentz-Dirac-like equations
67
0
0.0
(
0
)
Added by
Juan M. Aguirregabiria
Publication date
1997
fields
Physics
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
We discuss the phenomenon of preacceleration in the light of a method of successive approximations used to construct the physical order reduction of a large class of singular equations. A simple but illustrative physical example is analyzed to get more insight into the convergence properties of the method.
rate research
Read More
We study subsolutions of the Dirac and Duffin-Kemmer-Petiau equations described in our earlier papers. It is shown that subsolutions of the Duffin-Kemmer-Petiau equations and those of the Dirac equation obey the same Dirac equation with some built-in projection operator. This covariant equation can be referred to as supersymmetric since it has bosonic as well as fermionic degrees of freedom.
The well-known Greens function method has been recently generalized to nonlinear second order differential equations. In this paper we study possibilities of exact Greens function solutions of nonlinear differential equations of higher order. We show that, if the nonlinear term satisfies a generalized homogeneity property, then the nonlinear Greens function can be represented in terms of the homogeneous solution. Specific examples and a numerical error analysis support the advantage of the method. We show how, for the Bousinesq and Kortweg-de Vries equations, we are forced to introduce higher order Green functions to obtain the solution to the inhomogeneous equation. The method proves to work also in this case supporting our generalization that yields a closed form solution to a large class of nonlinear differential equations, providing also a formula easily amenable to numerical evaluation.
The singularity structure of a second-order ordinary differential equation with polynomial coefficients often yields the type of solution. If the solution is a special function that is studied in the literature, then the result is more manageable using the properties of that function. It is straightforward to find the regular and irregular singular points of such an equation by a computer algebra system. However, one needs the corresponding indices for a full analysis of the singularity structure. It is shown that the $theta$-operator method can be used as a symbolic computational approach to obtain the indicial equation and the recurrence relation. Consequently, the singularity structure which can be visualized through a Riemann P-symbol leads to the transformations that yield a solution in terms of a special function, if the equation is suitable. Hypergeometric and Heun-type equations are mostly employed in physical applications. Thus only these equations and their confluent types are considered with SageMath routines which are assembled in the open-source package symODE2.
In this paper we investigate the solution of generalized distributed order diffusion equations with composite time fractional derivative by using the Fourier-Laplace transform method. We represent solutions in terms of infinite series in Fox $H$-functions. The fractional and second moments are derived by using Mittag-Leffler functions. We observe decelerating anomalous subdiffusion in case of two composite time fractional derivatives. Generalized uniformly distributed order diffusion equation, as a model for strong anomalous behavior, is analyzed by using Tauberian theorem. Some previously obtained results are special cases of those presented in this paper.
We study the small-mass (overdamped) limit of Langevin equations for a particle in a potential and/or magnetic field with matrix-valued and state-dependent drift and diffusion. We utilize a bootstrapping argument to derive a hierarchy of approximate equations for the position degrees of freedom that are able to achieve accuracy of order $m^{ell/2}$ over compact time intervals for any $ellinmathbb{Z}^+$. This generalizes prior derivations of the homogenized equation for the position degrees of freedom in the $mto 0$ limit, which result in order $m^{1/2}$ approximations. Our results cover bounded forces, for which we prove convergence in $L^p$ norms, and unbounded forces, in which case we prove convergence in probability.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
