Related papers: New Revival Phenomena for Linear Integro-Different…
In this paper, the dispersive revival and fractalization phenomena for bidirectional dispersive equations on a bounded interval subject to periodic boundary conditions and discontinuous initial profiles are investigated. Firstly, we study…
Wave packet revivals and fractional revivals are striking quantum interference phenomena that can occur under suitable conditions in a system with a nonlinear spectrum. In the framework of a specific model (the propagation of an initially…
We examine the influence of quasi-periodic boundary conditions on the phenomenon of revivals in linear dispersive PDEs. We show that, in general, quasi-periodic problems do not support the revival effect at rational times. Our method is…
We develop a covariant formalism to study nonlinear perturbations of dissipative and interacting relativistic fluids. We derive nonlinear evolution equations for various covectors defined as linear combinations of the spatial gradients of…
The mysterious phenomena of revivals in linear dispersive periodic equations was discovered first experimentally in optics in the 19th century, then rediscovered several times by theoretical and experimental investigations. While the term…
A non-separable wave-like integro-differential equation for the time evolution of the Wigner distribution function in phase space is educed from the corresponding separable kinetic equation. It is shown that it leads to non-local dispersion…
We study the phenomenon of revivals for the linear Schr\"odinger and Airy equations over a finite interval, by considering several types of non-periodic boundary conditions. In contrast with the case of the linear Schr\"odinger equation…
We study Dirichlet-type problems for the simplest third-order linear dispersive PDE, often referred to as the Airy equation. Such problems have not been extensively studied, perhaps due to the complexity of the spectral structure of the…
The principal aim of this article is to establish an iteration method on the space of resurgent functions. We discuss endless continuability of iterated convolution products of resurgent functions and derive their estimates developing the…
The revival structure of wave packets is examined for quantum systems having energies that depend on two nondegenerate quantum numbers. For such systems, the evolution of the wave packet is controlled by two classical periods and three…
The dynamics of a quantum mechanical particle in a time-independent potential are found to contain many interesting phenomena. These are direct consequences of the (typical) existence of more than one time scale governing the problem. This…
In this overview paper, we show existence of smooth solitary-wave solutions to the nonlinear, dispersive evolution equations of the form \begin{equation*} \partial_t u + \partial_x(\Lambda^s u + u\Lambda^r u^2) = 0, \end{equation*} where…
In the paper, we discuss the reconstruction of scalar parameters in a linear diffusion equation with fractional in time differential operators and with additional nonlocal (convolution) terms, which incorporate memory effects in models.…
A novel mathematical nonlinear theory of surface gravity waves in deep water is presented, in which analytical analysis of the classical nonlinear equations of fluid dynamics is performed under less restrictive assumptions than those…
Biological and physical systems that can be classified as oscillatory media give rise to interesting phenomena like target patterns and spiral waves. The existence of these structures has been proven in the case of systems with local…
We present local existence theorem of the initial value problem for third order semilinear dispersive partial differential equations in two space dimensions. This type of equations arises in the study of gravity wave of deep water, and…
Wave packet revivals and fractional revivals are hallmark quantum interference phenomena that arise in systems with nonlinear energy spectra, and their signatures in expectation values of observables have been studied extensively in earlier…
In this article, we investigate the existence and properties of time-periodic solutions for damped evolutionary partial differential equations subject to periodic forcing. Particular emphasis is placed on configurations where the energy…
Paraxial wave packets with discrete spatial, temporal, or spatiotemporal spectra are known to undergo periodic axial revivals on propagation in either free space or linear transparent, weakly dispersive media. Such spectacular revivals,…
The paper is devoted to a reaction-diffusion equation with doubly nonlocal nonlinearity arising in various applications in population dynamics. One of the integral terms corresponds to the nonlocal consumption of resources while another one…