Related papers: Nonlinear interaction of waves in elastodynamics a…
This paper studies the stability and large-time behavior of the three-dimensional (3-D) Boltzmann equation near shock profiles. We prove the nonlinear stability of the composite wave consisting of two shock profiles under general…
We present a model for the dynamics of elastic or poroelastic bodies with monopolar repulsive long-range (electrostatic) interactions at large strains. Our model respects (only) locally the non-self-interpenetration condition but can cope…
Elastic turbulence is a spatially and temporally disordered flow state appearing in viscoelastic fluids at vanishing fluid inertia and large elasticity. The resulting flows have broad technological interest, particularly to enhance mixing…
In order to analyze numerically inverse problems several techniques based on linear and nonlinear stability analysis are presented. These techniques are illustrated on the problem of estimating mobilities and capillary pressure in…
Nonlinear dynamics of surface gravity waves trapped by an opposing jet current is studied analytically and numerically. For wave fields narrowband in frequency but not necessarily with narrow angular distributions the developed asymptotic…
In this paper, we study the stability and instability of plane wave solutions to semilinear systems of wave equations satisfying the null condition. We identify a condition which allows us to prove the global nonlinear asymptotic stability…
In this paper we derive nonlinear evolution equations associated with a class of non-convex energy functionals which can be used for correcting displacement errors in imaging data. We study properties of these filtering flows and provide…
We consider a problem of quantitative static elastography, the estimation of the Lam\'e parameters from internal displacement field data. This problem is formulated as a nonlinear operator equation. To solve this equation, we investigate…
We consider longwave mode of the interface instability in the system comprising of two immiscible fluid layers. The fluids fill out plane horizontal cavity which is subjected to horizontal harmonic vibration. The analysis is performed…
The instability and nonlinear evolution of directional ocean waves is investigated numerically by means of simulations of the governing kinetic equation for narrow-band surface waves. Our simulation results reveal the onset of the…
Kinetic numerical simulations of the evolution of the Weibel instability during the full nonlinear regime are presented. The formation of strong distortions in the electron distribution function resulting in formation of strong peaks in it…
We review the scattering from non-linear interfaces containing buckling elastic beams. An illustrative example is discussed here of scattering of linear elastic pressure waves from a two-mass system connected by a non-linear structured…
An ideal contrast-enhanced ultrasound image should display microbubble-induced nonlinearities while avoiding wave propagation nonlinearities. One of the most successful ultrasound pulse sequences to disentangle these nonlinear effects…
The modulational instability of nonlinearly interacting spatially incoherent Stokes waves is analyzed. Starting from a pair of nonlinear Schroedinger equations, we derive a coupled set of wave-kinetic equations by using the Wigner transform…
The coupled cubic nonlinear Schr\"odinger (CNLS) equations are used to study modulational instabilities of a pair of nonlinearly interacting two-dimensional waves in deep water. It has been shown that the full dynamics of these interacting…
Consider an exterior problem of the three-dimensional elastic wave equation, which models the scattering of a time-harmonic plane wave by a rigid obstacle. The scattering problem is reformulated into a boundary value problem by introducing…
The nonlinear dynamics of an obliquely oriented wave packet at sea surface is studied both analytically and numerically for various initial parameters of the packet, in connection with the problem of oceanic rogue waves. In the framework of…
The dynamics of gravitational waves is investigated in full 3+1 dimensional numerical relativity, emphasizing the difficulties that one might encounter in numerical evolutions, particularly those arising from non-linearities and gauge…
We consider the elastic wave scattering problem involving rigid obstacles. This work addresses the inverse problem of reconstructing the position and shape of such obstacles using far-field measurements. A novel monotonicity-based approach…
The effects of two-photon exchange corrections, suggested to explain the difference between measurements of the proton elastic electromagnetic form factors using the polarization transfer and Rosenbluth techniques, have been studied in…