Related papers: Nonlinear responses from the interaction of two pr…
We examine the transmission of quantum particles (phonons, electrons, and photons) across interfaces, identifying universal patterns in diverse physical scenarios. Starting with classical wave equations, we quantize them and derive kinetic…
A nonlinear Schr\"odinger equation with repulsive (defocusing) nonlinearity is considered. As an example, a system with a spatially varying coefficient of the nonlinear term is studied. The nonlinearity is chosen to be repelling except on a…
In granular media, the characterization of the behavior of solitary waves around interfaces is of importance in order to look for more applications of these systems. We study the behavior of solitary waves at both interfaces of a symmetric…
Periodically forced turbulence is used as a test case to evaluate the predictions of two-equation and multiple-scale turbulence models in unsteady flows. The limitations of the two-equation model are shown to originate in the basic…
We investigate new optical effects of nonlinear gravitational waves that arise from hereditary effects. Firstly, we show that the amplitude of continuous plane waves has a hereditary effect that grows with distance. This can make the…
We investigate the semilinear wave equation with potential on weighted graphs. We establish sufficient conditions for the nonexistence of global-in-time solutions. Both nonnegative and sign-changing solutions are considered. In particular,…
A localised overpressure translating at a uniform speed greater than a critical value acts at the interface between two deep fluid layers with different densities. We analyse the resulting wave patterns using an initial-value problem…
We construct solutions of nonlinear reaction-diffusion equations with nonlinear boundary conditions in spaces where the problem is supercritical and show the nonlinear balance required between the nonlinear terms in order to obtain a…
Recent studies have shown some unusual nonlinear dispersion behaviors that are disconnected from the linear regime. However, existing analytical techniques, such as perturbation methods, fail to correctly capture these behaviors. Here we…
Laboratory experimental results are presented for nonlinear Internal Solitary Waves (ISW) propagation in deep water configuration with miscible fluids. The results are validated against direct numerical simulations and traveling wave exact…
Some relationships, fundamental to the resolution of interface wave problems, are presented. These equations allow for the derivation of explicit secular equations for problems involving waves localized near the plane boundary of…
We consider the motion of a two-dimensional interface between air (above) and an irrotational, incompressible, inviscid, infinitely deep water (below), with surface tension present. We propose a new way to reduce the original problem into…
We apply the non-linear flow response formalism to the recently measured event plane correlations. We find that as a result of the combined effects of linear and non-linear flow response, the observed event plane correlations can be…
We consider a system of two reaction-diffusion-advection equations describing the one dimensional directed motion of particles with superimposed diffusion and mutual alignment. For this system we show the existence of traveling wave…
Ocean wind waves are a fundamental manifestation of complex dynamics in geophysical fluid systems, characterized by a rich interplay between dispersion and nonlinearity. While linear wave theory provides a first-order description of wave…
We report experiments on the full space and time resolved statistics of capillary wave turbulence at the air-water interface. The three-dimensional shape of the free interface is measured as a function of time by using the optical method of…
Nonlinear water waves interacting with quasi-one-dimensional, non-uniformly periodic bed profiles are studied numerically in the deep-water regime with the help of approximate equations for envelopes of the forward and backward waves.…
The Nonlinear Schr\"odinger (NLS) equation is widely used in everywhere of natural science. Various nonlinear excitations of the NLS equation have been found by many methods. However, except for the soliton-soliton interactions, it is very…
The three-layer Saffman-Taylor problem introduces two coupled moving interfaces separating the three fluids. A very recent weakly nonlinear analysis of this problem in a radial Hele-Shaw cell setup has shown that the morphologies of the…
In many plasma systems, introducing a small background shear flow is enough to stabilize the system linearly. The nonlinear dynamics are much less sensitive to sheared flows than the average linear growthrates, and very small amplitude…