Related papers: Interaction Dynamics of Singular Wave Fronts
We study travelling waves on a two--dimensional lattice with linear and nonlinear coupling between nearest particles and a periodic nonlinear substrate potential. Such a discrete system can model molecules adsorbed on a substrate crystal…
Pinning and depinning of wavefronts are ubiquitous features of spatially discrete systems describing a host of phenomena in physics, biology, etc. A large class of discrete systems is described by overdamped chains of nonlinear oscillators…
The concept of diffusion in collisionless space plasmas like those near the magnetopause and in the geomagnetic tail is reexamined from a fundamental statistical point of view making use of the division of particle orbits into waiting…
We compute time-periodic and relative-periodic solutions of the free-surface Euler equations that take the form of overtaking collisions of unidirectional solitary waves of different amplitude on a periodic domain. As a starting guess, we…
Solitons are localized nonlinear wave packets that propagate without spreading because nonlinearity balances dispersion. Their robustness is well understood in effectively one-dimensional systems, but introducing additional spatial…
Here we consider an integral equation describing a fixed number of scalar particles which interact not through boson exchange but directly along light cones, similarly as in bound state equations such as the Bethe-Salpeter equation. The…
The Euler-Poincar\'e differential (EPDiff) equations and the shallow water (SW) equations share similar wave characteristics. Using the Hamiltonian structure of the SW equations with flat bottom topography, we establish a connection between…
This paper considers the propagation of shallow-water solitary and nonlinear periodic waves over a gradual slope with bottom friction in the framework of a variable-coefficient Korteweg-de Vries equation. We use the Whitham averaging…
The early phase of the hydrodynamic evolution following collision of two stars is analyzed. Two strong shocks propagate at a constant velocity (which is a small fraction of the velocity of the approaching stars) from the contact surface…
This paper is concerned with the study of interaction of waves originating from the Riemann problem centred at two different points for a system of equations modelling propagation of elastic waves. The system consists of two equations for…
The interaction of localised solitary waves with large-scale, time-varying dispersive mean flows subject to nonconvex flux is studied in the framework of the modified Korteweg-de Vries (mKdV) equation, a canonical model for nonlinear…
An interface between two media is topologically stable two-dimensional object where 3D-symmetry breaks which allows for existence of many exotic excitations. A direct way to explore surface excitations is to investigate their interaction…
Flow networks are fundamental for understanding systems such as animal and plant vasculature or power distribution grids. These networks can encode, transmit, and transform information embodied in the spatial and temporal distribution of…
Changing the microstructure properties of a space-time metamaterial while a wave is propagating through it, in general requires addition or removal of energy, which can be of exponential form depending on the type of modulation. This limits…
Further development of the method of quantum hydrodynamics in application for Bose-Einstein condensates (BECs) is presented. To consider evolution of polarization direction along with particles movement we have developed corresponding set…
We analyze the propagation properties of the numerical versions of one and two-dimensional wave equations, semi-discretized in space by finite difference schemes. We focus on high-frequency solutions whose propagation can be described, both…
We study the propagation of monochromatic surface waves on a turbulent flow. The flow is generated in a layer of liquid metal by an electromagnetic forcing. This forcing creates a quasi two-dimensional (2D) turbulence with strong vertical…
In most classical fluids, shock waves are strongly dissipative, their energy being quickly lost through viscous damping. But in systems such as cold plasmas, superfluids, and Bose-Einstein condensates, where viscosity is negligible or…
In this experimental study, we investigate the interaction of gravity-capillary solitary waves generated by two surface pressure sources moving side by side at constant speed. The nonlinear response of a water surface to a single source…
The nonlinear propagation of electrostatic solitary waves is studied in a collisionless electron-positron pair plasma consisting of adiabatic cool electrons, mobile cool positrons (or electron holes), hot suprathermal electrons described by…