We study the dynamics of a quantum particle in R n+m constrained by a strong potential force to stay within a distance of order (in suitable units) from a smooth n−dimensional submanifold M. We prove that in the semiclassical limit the evolution of the wave function is approximated in norm, up to terms of order 1/2 , by the evolution of a semiclassical wave packet centred on the trajectory of t...

In this work, recently deduced generalized Kudryashov method is applied to the variant Boussinesq equations, and the (2 + 1)-dimensional breaking soliton equations. As a result a range of qualitative explicit exact traveling wave solutions are deduced for these equations, which motivates us to develop, in the near future, a new approach to obtain unsteady solutions of autonomous nonlinear evolu...

Picosecond laser pulses have been used to produce Rydberg wave packets in calcium atoms in the presence of a strong static electric field. The dynamics of the Stark wave packets have been observed by measuring the momentum-space probability distribution as a function of time. The full precession of the electronic orbital angular momentum, the appearance of a large-amplitude, linear oscillation ...

This work continues our studies of nonlinear evolution of a system of wavepackets. We study a wave propagation governed by a nonlinear system of hyperbolic PDE's with constant coefficients with the initial data being a multi-wavepacket. By definition a general wavepacket has a well defined principal wave vector, and, as we proved in previous works, the nonlinear dynamics preserves systems of wa...

This work continues our studies of nonlinear evolution of a system of wavepackets. We study a wave propagation governed by a nonlinear system of hyperbolic PDE's with constant coefficients with the initial data being a multi-wavepacket. By definition a general wavepacket has a well defined principal wave vector, and, as we proved in previous works, the nonlinear dynamics preserves systems of wa...

Since the pioneering experiment by the father-son team of the Kapitza family during their house arrest in the late forties (Kapitza & Kapitza 1949), wave evolution on a falling film has intrigued many researchers. One of its main attractions is its simplicity-it is an open-flow hydrodynamic instability that occurs at very low flow rates. It can hence be studied with the simplest experimental ap...

Using a previously undescribed approach, we develop an analytic model that predicts whether an asexual population accumulates advantageous or deleterious mutations over time and the rate at which either process occurs. The model considers a large number of linked identical loci, or nucleotide sites; assumes that the selection coefficient per site is much less than the mutation rate per genome; ...

Hydrodynamic derivation of the entrainment of matter induced by a surface elastic wave propagating along the flexible vacuum-matter interface is conducted by considering the nonlinear coupling between the interface and the rarefaction effect. The critical reflux values associated with the product of the second-order (unit) body forcing and the Reynolds number (representing the viscous dissipati...

In this paper, we present a numerical scheme for the propagation of acoustic waves in a heterogeneous medium in the context of the finite volume evolution Galerkin (FVEG) method (M. Lukáčová-Medvid’ová et al. J. Comput. Phys., 183:533–562, 2002). As a mathematical model we consider a wave equation system with space dependent wave-speed and impedance, which is used to study the wave propagation ...

This work examines the extent to which a few basic concepts that apply to plane waves, for example, the refraction of waves up the gradient of the index of refraction, apply to stratospheric planetary waves. This is done by studying the relation between group velocity (Cg) and the wave activity velocity, which is defined as the Eliassen–Palm flux divided by the wave activity density (Va 5 F/A)....