We present a numerical investigation of the tunneling dynamics of a particle moving in a bistable potential with fluctuating barrier which is coupled to a non-integrable classical system and study the interplay between classical chaos and barrier fluctuation in the tunneling dynamics. We found that the coupling of the quantum system with the classical subsystem decreases the tunneling rate irrespective of whether the classical subsystem is regular or chaotic and also irrespective of the fact that whether the barrier fluctuates or not. Presence of classical chaos always enhances the tunneling rate constant. The effect of barrier fluctuation on the tunneling rate in a mixed quantum-classical system is to suppress the tunneling rate. In contrast to the case of regular subsystem, the suppression arising due to barrier fluctuation is more visible when the subsystem is chaotic.

We make use of a coordinate-free approach to implement Vakhitov–Kolokolov criterion for stability analysis in order to study the effects of three-body atomic recombination and lattice potential on the matter–wave bright solitons formed in Bose–Einstein condensates. We analytically demonstrate that (i) the critical number of atoms in a stable BEC soliton is just half the number of atoms in a marginally stable Townes-like soliton and (ii) an additive optical lattice potential further reduces this number by a factor of $\sqrt{1 − b_{g3}$ with $g_{3}$ the coupling constant of the lattice potential and $b = 0.7301$.

An expression for the transition probability or form factor in one-dimensional Rydberg atom irradiated by short half-cycle pulse was constructed. In applicative contexts, our expression was found to be more useful than the corresponding result given by Landau and Lifshitz. Using the new expression for the form factor, the motion of a localized quantum wave packet was studied with particular emphasis on its revival and super-revival properties. Closed form analytical expressions were derived for expectation values of the position and momentum operators that characterized the widths of the position and momentum distributions. Transient phase-space localization of the wave packet produced by the application of a single impulsive kick was explicitly demonstrated. The undulation of the uncertainty product as a function of time was studied in order to visualize how the motion of the wave packet in its classical trajectory spreads throughout the orbit and the system becomes nonclassical. The process, however, repeats itself such that the atom undergoes a free evolution from a classical, to a nonclassical, and back to a classical state.

We examine the effect of dissipation on travelling waves in nonlinear dispersive systems modelled by Benjamin–Bona–Mahony (BBM)-like equations. In the absence of dissipation, the BBM-like equations are found to support soliton and compacton/anticompacton solutions depending on whether the dispersive term islinear or nonlinear. We study the influence of increasing nonlinearity of the medium on the soliton and compacton dynamics. The dissipative effect is found to convert the solitons either to undular bores or to shock-like waves depending on the degree of nonlinearity of the equations. The anticompacton solutions are also transformed to undular bores by the effect of dissipation. But the compactons tend to vanish due to viscous effects. The local oscillatory structures behind the bores and/or shock-like waves in the case of solitons and anticompactons are found to depend sensitively both on the coefficient of viscosity and solution of the unperturbed problem.