ar X iv :p hy si cs /0 60 70 59 v 1 7 Ju l 2 00 6 Abstract This paper presents theoretical results indicating that newly discovered nondiffracting beams we call X waves, can propagate in a confined space (wave guide) with specific quantized temporal frequencies. These results could have applications in nondispersive transmission of acoustic, electromagnetic (microwaves) and optical energy throu...

Using a generalized transfer matrix method we exactly solve the Schrödinger equation in a time periodic potential, with discretized Euclidean space-time. The ground state wave function propagates in space and time with an oscillating soliton-like wave packet and the wave front is wedge shaped. In a statistical mechanics framework our solution represents the partition sum of a directed polymer s...

The approach is based on a pragmatic view of naturally occurring quantum systems, referred to in this paper as Wave Packet Network (WPN) theory. This pragmatic view of quantum mechanics interprets large classical systems as multi-scale networks of wave packets. Exchanges of information between pairs of WPN packets cause both packets to restructure (―collapse‖) in ways that restrict the sets of ...

We investigate how the non-analytic solitary wave solutions | peakons and compactons | of an integrable biHamiltonian system arising in uid mechanics, can be recovered as limits of classical solitary wave solutions forming analytic homoclinic orbits for the reduced dynamical system. This phenomenon is examined to understand the important eeect of linear dispersion terms on the analyticity of su...

-In this paper a parabolic equation with memory operator is considered. CNN model for such equation is made. Dynamic behavior of the CNN model is studied using describing function method. Traveling wave solutions are proved for the CNN model. An example of one-dimensional wave in medium with memory arising in classical mechanics is presented. Key-Words:Cellular Neural Networks, Partial Differen...

The Schrödinger equation with the nonlinear term −b(ln |Ψ|2)Ψ is derived by the natural generalization of the hydrodynamical model of quantum mechanics. The nonlinear term appears to be logically necessary because it enables explanation of the classical limit of the wave function, the collaps of the wave function and solves the Schrödinger cat paradox.

In this paper, we use two different integral techniques, the first integral and the direct integral method, to study the variable coefficient nonlinear Schrödinger (NLS) equation arising in arterial mechanics. The application of the first integral method yielded periodic and solitary wave solutions. Using the direct integration lead to solitary wave solution and Jacobi elliptic function solutions.

We investigate how the non-analytic solitary wave solutions — peakons and compactons — of an integrable biHamiltonian system arising in fluid mechanics, can be recovered as limits of classical solitary wave solutions forming analytic homoclinic orbits for the reduced dynamical system. This phenomenon is examined to understand the important effect of linear dispersion terms on the analyticity of...

The concepts of quantile position, trajectory, and velocity are defined. For a tunneling quantum mechanical wave packet, it is proved that its quantile position always stays behind that of a free wave packet with the same initial parameters. In quantum mechanics the quantile trajectories are mathematically identical to Bohm’s trajectories. A generalization to three dimensions is given.

Denoting by v ̄ the velocity flow of a classical particle that is subject to a potential V , we demonstrate that the path-integral formalism of non-relativistic quantum mechanics can be obtained by superimposing wave functions that are solutions of a wave equation which in turn directly corresponds to the probability conservation equation div(ψ∗ψv ̄ ) = 0.