Related papers: The Dirac-Delta Rogue Wave
We analytically investigate the nonautonomous discrete rogue wave solutions and their interaction in the generalized Ablowitz-Ladik-Hirota lattice with variable coefficients, which possess complicated wave propagations in time and are…
We present a mathematical approach that simplifies the theoretical treatment of electromagnetic localization in random media and leads to closed form analytical solutions. Starting with the assumption that the dielectric permittivity of the…
Wave propagation in time-varying media has attracted significant attention for its innovative potential to control wave-matter interactions and to develop versatile active materials. While most research has focused on electromagnetic waves,…
We solve the one-dimensional Dirac equation by taking into account the possibility of position-dependence in the mass function. We also take the Fermi velocity to act as a local variable and examine the combined effects of the two on the…
A non-perturbative approach to the solution of the time-dependent, two-center Dirac equation is presented with a special emphasis on the proper treatment of the potential of the nuclei. In order to account for the full multipole expansion…
We construct rogue wave solutions on the double periodic background for the Hirota equation through one fold Darboux transformation formula. We consider two types of double periodic solutions as seed solutions. We identify the squared…
A set of traveling wave solution to convection-reaction-diffusion equation is studied by means of methods of local nonlinear analysis and numerical simulation. It is shown the existence of compactly supported solutions as well as solitary…
We demonstrate a way to generate a two-dimensional rogue waves in two types of broad area nonlinear optical systems subject to time-delayed feedback: in the generic Lugiato-Lefever model and in model of a broad-area surface-emitting laser…
This article investigates some solutions of the time-dependent free Dirac equation. Visualizations of these solutions immediately reveal strange phenomena that are caused by the interference of positive- and negative-energy waves. The…
Wave localization induced by spatial disorder is ubiquitous in physics. Here, we study the temporal analog of such phenomenon on water waves. Our time disordered media consists in a collection of temporal interfaces achieved through…
In this work, we explore the rogue wave patterns in the coupled Fokas-Lenells equation by using the Darboux transformation. We demonstrate that when one of the internal parameters is large enough, the general high-order rogue wave solutions…
Localized solutions of the Dirac equation for an electron moving in free space and electromagnetic field lattices with periodic dependence on space-time coordinates (electromagnetic space-time crystals) are treated using the expansions in…
The fundamental solution of the Dirac equation for an electron in an electromagnetic field with harmonic dependence on space-time coordinates is obtained. The field is composed of three standing plane harmonic waves with mutually orthogonal…
In this essay we give an overview on the problem of rogue or freak wave formation in the ocean. The matter of the phenomenon is a sporadic occurrence of unexpectedly high waves on the sea surface. These waves cause serious danger for…
We systematically investigate rogue wave's spatial-temporal pattern in $N$ $(N\geq2)$-component coupled defocusing nonlinear Schr\"{o}dinger equations. The fundamental rogue wave solutions are given in a unified form for both focusing and…
The validation and parallel implementation of a numerical method for the solution of the time-dependent Dirac equation is presented. This numerical method is based on a split operator scheme where the space-time dependence is computed in…
We present exact solutions for rogue waves arising on the background of periodic waves in the focusing nonlinear Schrodinger equation. The exact solutions are obtained by characterizing the Lax spectrum related to the periodic waves and by…
In the present article, using a further generalization of the algebraic method of separation of variables, the Dirac equation is separated in a family of space-times where it is not possible to find a complete set of first order commuting…
We propose to construct a temporary wave on the surface of the ocean, as a particular solution of the Saint-Venant equations with a source term involving the friction, whose shape is expected to mimic a rogue wave.
In this presentation, we analytically derive the dispersion equation for surface waves traveling along reactive boundaries which are periodically modulated in time. In addition, we show numerical results for the dispersion curves and…