Related papers: Stable numerical coupling of exterior and interior…
In this paper we use the short-wavelength instability approach to derive an instability threshold for exact trapped equatorial waves propagating eastwards in the presence of an underlying current.
In this paper, we recast the variational formulation corresponding to the single layer boundary integral operator $\operatorname{V}$ for the wave equation as a minimization problem in $L^2(\Sigma)$, where $\Sigma := \partial \Omega \times…
In this paper, we establish the existence and instability of standing wave for a system of nonlinear Schr\"{o}dinger equations arising in the two-wave model with quadratic interaction in higher space dimensions under mass resonance…
We numerically study solitary waves in the coupled nonlinear Schr\"odinger equations. We detect pitchfork bifurcations of the fundamental solitary wave and compute eigenvalues and eigenfunctions of the corresponding eigenvalue problems to…
We consider a system of nonlinear Klein-Gordon equations with quadratic interaction in two and three space dimensions. The strong instability of standing wave solutions is studied for the system without assuming the mass resonance…
A simple generalization of the Swift-Hohenberg equation is proposed as a model for the pattern-forming dynamics of a two-dimensional field with two unstable length scales. The equation is used to study the dynamics of surface waves in a…
We derive a new generalization of the nonlinear variational wave equation. We prove existence of local, smooth solutions for this system. As a limiting case, we recover the nonlinear variational wave equation.
The periodic standing-wave method for binary inspiral computes the exact numerical solution for periodic binary motion with standing gravitational waves, and uses it as an approximation to slow binary inspiral with outgoing waves. Important…
We study the instability of standing waves for nonlinear Schr\"{o}dinger equations. Under a general assumption on nonlinearity, we prove that linear instability implies orbital instability in any dimension. For that purpose, we establish a…
We consider both the internal and boundary controllability problems for wave equations under non-negativity constraints on the controls. First, we prove the steady state controllability property with nonnegative controls for a general class…
In this article we shall go over recent work in proving dispersive and Strichartz estimates for the Dirichlet-wave equation. We shall discuss applications to existence questions outside of obstacles and discuss open problems.
In this paper we consider the spectral and nonlinear stability of periodic traveling wave solutions of a generalized Kuramoto-Sivashinsky equation. In particular, we resolve the long-standing question of nonlinear modulational stability by…
An ill-posed Cauchy problem for the wave equation is considered: the solution is to be determined by the Cauchy data on some part of the time-space boundary. By means of Fourier method we obtain a regularization algorithm for this problem,…
We consider the inverse dynamic problem for the wave equation with a potential on an interval $(0,2\pi)$ with periodic boundary conditions. We use a boundary triplet to set up the initial-boundary value problem. As an inverse data we use a…
This paper addresses the output regulation problem for a one-dimensional unstable wave equation subject to output delay and all-channel disturbances with unknown frequencies and amplitudes. First, this problem is transformed into a…
When simulating resistive-capacitive circuits or electroquasistatic problems where conductors and insulators coexist, one observes that large time steps or low frequencies lead to numerical instabilities, which are related to the condition…
Two page encyclopedic article about the Korteweg-de Vries equation covering historical perspective, solitary wave and periodic solutions, modern developments, properties and applications, and further reading.
We obtain the most general matrix criterion for stability and instability of multi-component solitary waves considering a system of $N$ incoherently coupled nonlinear Schrodinger equations. Soliton stability is studied as a constrained…
An initial-boundary value problem for the $n$-dimensional wave equation is considered. A three-level explicit in time and conditionally stable 4th-order compact scheme constructed recently for $n=2$ and the square mesh is generalized to the…
This paper focuses on stability estimates of the inverse random source problems for the polyharmonic, electromagnetic, and elastic wave equations. The source is represented as a microlocally isotropic Gaussian random field, which is defined…