Related papers: A complete and partial integrability technique of …
This letter suggests a new way to investigate 3-D chaos in spatial and frequency domains simultaneously. After spatially decomposing the Lorenz attractor into two separate scrolls with peaked spectra and a 1-D discrete-time zero-crossing…
This paper presents a unifying theory of Linear second order systems that allows time-varying and time invariant systems to be treated in the same way for the first time. In the process, a transformation is given that diagonalizes an…
A method of representation of a solution as segments of the series in powers of the step of the independent variable is expanded for solving complex systems of ordinary differential equations (ODE): the Lorenz system and other systems. A…
It is is explained why physical consistency requires substituting linear observables by nonlinear ones for quantum systems with nonlinear time evolution of pure states. The exact meaning and the concrete physical interpretation are…
The dynamics of unidirectionally coupled chaotic Lorenz systems is investigated. It is revealed that chaos is present in the response system regardless of generalized synchronization. The presence of sensitivity is theoretically proved, and…
Non-autonomous dynamical systems help us to understand the implications of real systems which are in contact with their environment as it actually occurs in nature. Here, we focus on systems where a parameter changes with time at small but…
In the present study, we analyze in combination the principles of special relativity and the phenomenon of the aberration of light, deriving a system of equations that allows establishing the relationship between the angles commonly…
Starting from a generic generally covariant classical theory we introduce the logarithmic correction to the quantum wave equation. We demonstrate the emergence of the evolution time from the group of automorphisms of the von Neumann algebra…
Euler's three-body problem is the problem of solving for the motion of a particle moving in a Newtonian potential generated by two point sources fixed in space. This system is integrable in the Liouville sense. We consider the Euler problem…
A quantum gravity theory which becomes renormalizable at short distances due to a spontaneous symmetry breaking of Lorentz invariance and diffeomorphism invariance is studied. A breaking of Lorentz invariance with the breaking patterns…
In dealing with nonlinear systems, it is common to use numerical solutions. Unlike the careful behavior towards the numerical results in chaotic regions, the validity of numerical results in regions of transient chaos might not always be…
A method of expansion of solutions of singularly perturbed nonlinear systems in power series of small parameters is applied to the popular Lorenz model in synergetics.Simple asymptotic expressions for the solution to the model in…
Some intriging connections between the properties of nonlinear noise driven systems and the nonlinear dynamics of a particular set of Hamilton's equation are discussed. A large class of Fokker-Planck Equations, like the Schr\"odinger…
In this paper we have chosen to work with two different approaches to solving the inverse problem of the calculus of variation. The first approach is based on an integral representation of the Lagrangian function that uses the first…
The scalar nonlinear Schrodinger (NLS) equation and a suitable discretization are well known integrable systems which exhibit the phenomena of ``effective'' chaos. Vector generalizations of both the continuous and discrete system are…
Coupling light to ensembles of strongly interacting particles has emerged as a promising route toward achieving few photon nonlinearities. One specific way to implement this kind of nonlinearity is to interface light with highly excited…
We discuss the unstable character of the solutions of the Lorentz-Dirac equation and stress the need of methods like order reduction to derive a physically acceptable equation of motion. The discussion is illustrated with the paradigmatic…
The Lorentz symmetry group entails physical equations whose solutions are retarded. This leads to the concept of a relativistic engine resulting from retardation of electromagnetic fields. We have shown that Newton'n third law cannot…
There exist several approaches that investigate the connectedness of spacetime events through solutions of the Lorentz force equation. These approaches separate into three categories, that consider different equations. We clarify the…
In the paper we investigate the theory of quantum optical systems. As an application we integrate and describe the quantum optical systems which are generically related to the classical orthogonal polynomials. The family of coherent states…