相关论文: Stable numerical coupling of exterior and interior…

We perform full-scale numerical simulation of instability of weakly nonlinear waves on the surface of deep fluid. We show that the instability development leads to chaotization and formation of wave turbulence. We study instability both of…

Stability of travelling waves for the Nagumo equation on the whole line is proven using a new approach via functional inequalities and an implicitely defined phase adaption. The approach can be carried over to obtain pathwise stability of…

We consider wave models with lower order terms and recollect some recent results on energy and dispersive estimates for their solution based on symbolic type estimates for coefficients and partly stabilisation conditions. The exposition is…

A large class of multidimensional nonlinear Schroedinger equations admit localized nonradial standing wave solutions that carry nonzero intrinsic angular momentum. Here we provide evidence that certain of these spinning excitations are…

Wave propagation in curved tubular domains is considered. A general version of Webster's equation is derived from the scattering passive wave equation. More precisely, it is shown that planar averages of a sufficiently smooth solution of…

In this paper, we determine the spectral instability of periodic odd waves for the defocusing fractional cubic nonlinear Schr\"odinger equation. Our approach is based on periodic perturbations that have the same period as the standing wave…

We prove local unique solvability of the wave equation for a large class of weakly singular, locally bounded space-time metrics in a suitable space of generalised functions.

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…

Boundary integral equation is derived for the problem of scattering of electromagnetic waves by 3D homogeneous body of arbitrary shape.

We show that periodic traveling waves with sufficiently small amplitudes of the Whitham equation, which incorporates the dispersion relation of surface water waves and the nonlinearity of the shallow water equations,are spectrally unstable…

We consider several different bidirectional Whitham equations that have recently appeared in the literature. Each of these models combine the full two-way dispersion relation from the incompressible Euler equations with a canonical shallow…

A parabolic equation for the propagation of periodic internal waves over varying bottom topography is derived using the multiple-scale perturbation method. Some computational aspects of the numerical implementation are discussed. The…

In this paper we consider the mixed problem for the wave equation exterior to a non-trapping obstacle in odd space dimensions. We derive a rate of the convergence of the solution for the mixed problem to a solution for the Cauchy problem.…

A review of the author's results is given. Inversion formulas and stability estimates for the solutions to 3D inverse scattering problems with fixed-energy data are obtained. Inversions of exact and noisy data are stidied. The inverse…

New travelling wave solutions to the Fornberg-Whitham equation are investigated. They are characterized by two parameters. The expresssions for the periodic and solitary wave solutions are obtained.

We study a system of nonlinear Schr\"odinger equations with cubic interactions in one space dimension. The orbital stability and instability of semitrivial standing wave solutions are studied for both non-degenerate and degenerate cases.

We study wave turbulence in systems with two special properties: a large number of fields (large $N$) and a nonlinear interaction that is strongly local in momentum space. The first property allows us to find the kinetic equation at all…

The classical numerical methods play important roles in solving wave equation, e.g. finite difference time domain method. However, their computational domain are limited to flat space and the time. This paper deals with the description of…

In this paper, we investigate the spectral stability of periodic traveling waves for a cubic-quintic and double dispersion equation. Using the quadrature method we find explict periodic waves and we also present a characterization for all…

It is proved that if the scattering amplitudes at a fixed wavenumber for two obstacles from a certain large class of obstacles differ a little, than the obstacles differ a little. Error estimate is given. It is proved that there is an…