Related papers: Nonlinear wave interactions in geochemical modelin…
Within the framework of the thermal wave model, an investigation is made of the longitudinal dynamics of high energy charged particle beams. The model includes the self-consistent interaction between the beam and its surroundings in terms…
We consider the complete Euler system describing the time evolution of an inviscid non-isothermal gas. We show that the rarefaction wave solutions of the 1D Riemann problem are stable, in particular unique, in the class of all bounded weak…
This article investigates the numerical solution of the Diffusive Wave equation posed on domains containing a large number of polygonal perforations, motivated by urban flood modeling. Such geometries induce strong multiscale effects driven…
We consider the modulational instability of nonlinearly interacting two-dimensional waves in deep water, which are described by a pair of two-dimensional coupled nonlinear Schroedinger equations. We derive a nonlinear dispersion relation.…
We consider general parameter to solution maps $\theta \mapsto \mathcal G(\theta)$ of non-linear partial differential equations and describe an approach based on a Banach space version of the implicit function theorem to verify the gradient…
The resonant interaction of relativistic electrons and whistler waves is an important mechanism of electron acceleration and scattering in the Earth radiation belts and other space plasma systems. For low amplitude waves, such an…
Surface water waves in ideal fluids have been typically modeled by asymptotic approximations of the full Euler equations. Some of these simplified models lose relevant properties of the full water wave problem. One of them is the Galilean…
Integrity of layered structures, extensively used in modern industry, strongly depends on the quality of their interfaces; poor adhesion or delamination can lead to a failure of the structure. Can nonlinear waves help us to control the…
Massively-parallel molecular dynamics simulation is applied to systems containing electrolytes, vapour-liquid interfaces, and biomolecules in contact with water-oil interfaces. Novel molecular models of alkali halide salts are presented and…
Optomechanical manipulation of nanoparticles enabling ultimate control over their 3D motion is nowadays one of the most highly demanded links between optics, biology, medicine, microfluidics, etc., paving the way for a plethora of emerging…
The free interface separating an exterior, viscous fluid from an intrusive conduit of buoyant, less viscous fluid is known to support strongly nonlinear solitary waves due to a balance between viscosity-induced dispersion and…
Wind forcing of the ocean generates a spectrum of inertia-gravity waves that is sharply peaked near the local inertial (or Coriolis) frequency. The corresponding near-inertial waves (NIWs) are highly energetic and play a significant role in…
The analysis of nonlinear wave equations has experienced a dramatic growth in the last ten years or so. The key factor in this has been the transition from linear analysis, first to the study of bilinear and multilinear wave interactions,…
The phenomenon of nonlinear wave mixing is investigated in a Yukawa one-component plasma using two-dimensional classical Langevin molecular dynamics simulations. The wave spectrum indicates that nonlinear interactions between the excited…
We rigorously show that a class of systems of partial differential equations modeling wave bifurcations supports stationary equivariant bifurcation dynamics through deriving its full dynamics on the center manifold(s). A direct consequence…
In this paper, we investigate the global structure of solutions to the Cauchy problem for the scalar viscous conservation law where the far field states are prescribed. Especially, we deal with the case when the viscous/diffusive flux…
The diffraction of a plane wave by a transversely inhomogeneous isotropic nonmagnetic linearly polarized dielectric layer filled with a Kerr-type nonlinear medium is considered. The analytical and numerical solution techniques are…
We investigate a laser model for a resonant system of photons and ion cluster-solvated rotating water molecules in which ions in the cluster are identical and have very low, non-relativistic velocities and direction of motion parallel to a…
The boundary problem of linear classical optics about the interaction of electromagnetic radiation with a thin dielectric film has been solved under explicit consideration of its discrete structure. The main attention has been paid to the…
Reactive infiltration instability (RII) drives the development of many natural and engineered flow systems. These are encountered e.g. in hydraulic fracturing, geologic carbon storage and well stimulation in enhanced oil recovery. The…