Related papers: Nonlinear dispersion in wave-current interactions
The three-wave resonant interaction equations are a non-dispersive system of partial differential equations with quadratic coupling describing the time evolution of the complex amplitudes of three resonant wave modes. Collisions of wave…
A new variational theory is presented for beam loading in microwave cavities. The beam--field interaction is formulated as a dynamical interaction whose stationarity according to Hamilton's principle will naturally lead to steady-state…
The Sagdeev-Zaslavski (SZ) equation for wave turbulence is analytically derived, both in terms of generating function and of multi-point pdf, for weakly interacting waves with initial random phases. When also initial amplitudes are random,…
This is the full and extended version of the brief note arXiv:1908.00938. A nontrivially solvable 4-dimensional Hamiltonian system is applied to the problem of wave fronts and to the asymptotic theory of partial differential equations. The…
This study deals with continuous limits of interacting one-dimensional diffusive systems, arising from stochastic distortions of discrete curves with various kinds of coding representations. These systems are essentially of a…
We apply Poisson reduction techniques to describe asymptotic fully nonlinear models of fluid wave motion in the Hamiltonian setting. We start by considering Zakharov and Benjamin Hamiltonian settings for a stably stratified $2D$ Euler…
A bouncing droplet on a vibrated bath can couple to the waves it generates, so that it becomes a propagative walker. Its propulsion at constant velocity means that a balance exists between the permanent input of energy provided by the…
A new asymptotic method is presented for the analysis of the traveling waves in the one-dimensional reaction-diffusion system with the diffusion with a finite velocity and Kolmogorov-Petrovskii-Piskunov kinetics. The analysis makes use of…
We study the diffusion phenomena on the negatively curved surface made up of congruent heptagons. Unlike the usual two-dimensional plane, this structure makes the boundary increase exponentially with the distance from the center, and hence…
We study the waves at the interface between two thin horizontal layers of immiscible fluids subject to high-frequency horizontal vibrations. Previously, the variational principle for energy functional, which can be adopted for treatment of…
We introduce a simplified model for wave turbulence theory -- the Wick NLS, of which the main feature is the absence of all self-interactions in the correlation expansions of its solutions. For this model, we derive several wave kinetic…
A unified electrodynamic approach to the guided-wave excitation theory is generalized to the waveguiding structures containing a hypothetical space-dispersive medium with drifting charge carriers possessing simultaneously elastic,…
A notorious difficulty in the covariant dynamics of classical charged particles subject to non-local electromagnetic (EM) interactions arising in the EM radiation-reaction (RR) phenomena is due to the definition of the related non-local…
The Whitham equation was proposed as an alternate model equation for the simplified description of uni-directional wave motion at the surface of an inviscid fluid. As the Whitham equation incorporates the full linear dispersion relation of…
This paper is devoted to the derivation and mathematical analysis of a wave-structure interaction problem which can be reduced to a transmission problem for a Boussinesq system. Initial boundary value problems and transmission problems in…
Shallow water waves are a striking example of nonlinear hydrodynamics, giving rise to phenomena such as tsunamis and undular waves. These dynamics are typically studied in hundreds-of-meter-long wave flumes. Here, we demonstrate a…
By an idealized quantum mechanical model, we formally describe the dispersion of nonretarded electromagnetic waves that express charge density oscillations near a fixed plane in three spatial dimensions (3D) at zero temperature. Our goal is…
We introduce and systematically investigate the generation of dispersive shock waves, which arise naturally in physical settings such as optical waveguide arrays and superfluids confined within optical lattices. The underlying physically…
Classical viscid media are quite common in our everyday life. However, we are not used to find such media in quantum mechanics, and much less to analyze their effects on the dynamics of quantum systems. In this regard, the Caldirola-Kanai…
We study traveling wave solutions of an equation for surface waves of moderate amplitude arising as a shallow water approximation of the Euler equations for inviscid, incompressible and homogenous fluids. We obtain solitary waves of…