Related papers: Explicit Dirichlet-neumann Operator For Water Wave…
We evaluate the spectral determinant for the damped wave equation on an interval of length $T$ with Dirichlet boundary conditions, proving that it does not depend on the damping. This is achieved by analysing the square of the damped wave…
Based on explicit computations, various concepts of discrete time scattering theory are reviewed, discussed, and illustrated. The dynamics are taking place on a discrete half-space. All operators are represented graphically. The expressions…
We study a Dirichlet-to-Neumann eigenvalue problem for differential forms on a compact Riemannian manifold with smooth boundary. This problem is a natural generalization of the classical Steklov problem on functions. We derive a number of…
We present a Waveform Relaxation (WR) version of the Dirichlet-Neumann and Neumann-Neumann algorithms for the wave equation in space time. Each method is based on a non-overlapping spatial domain decomposition, and the iteration involves…
An explicit formula for the wave operators associated with Schroedinger operators on the discrete half-line is deduced from their stationary expressions. The formula enables us to understand the wave operators as one dimensional…
In this paper, we propose a strategy to determine the Dirichlet-to-Neumann (DtN) operator for infinite, lossy and locally perturbed hexagonal periodic media. We obtain a factorization of this operator involving two non local operators. The…
The formulation of a canonical deep-water breaking wave problem is introduced, and the results of a set of three-dimensional numerical simulations for deep-water breaking waves are presented. In this paper fully nonlinear progressive waves…
The use of operator methods of algebraic nature is shown to be a very powerful tool to deal with different forms of relativistic wave equations. The methods provide either exact or approximate solutions for various forms of differential…
A general representation formula for the scattering matrix of a scattering system consisting of two self-adjoint operators in terms of an abstract operator valued Titchmarsh-Weyl $m$-function is proved. This result is applied to scattering…
Numerical simulations of seismic wave propagation in heterogeneous 3D media are central to investigating subsurface structures and understanding earthquake processes, yet are computationally expensive for large problems. This is…
We formulate a new family of high order on-surface radiation conditions to approximate the outgoing solution to the Helmholtz equation in exterior domains. Motivated by the pseudo-differential expansion of the Dirichlet-to-Neumann operator…
We study normal modes for the linear water wave problem in infinite straight channels of bounded constant cross-section. Our goal is to compare semianalytic normal mode solutions known in the literature for special triangular…
The dynamics of solitary gravity-capillary water waves propagating on the surface of a three-dimensional fluid domain is studied numerically. In order to accurately compute complex time dependent solutions, we simplify the full potential…
This paper is concerned with a priori $C^\infty$ regularity for three-dimensional doubly periodic travelling gravity waves whose fundamental domain is a symmetric diamond. The existence of such waves was a long standing open problem solved…
We consider an extension of the methodology of the modified method of simplest equation to the case of use of two simplest equations. The extended methodology is applied for obtaining exact solutions of model nonlinear partial differential…
Reduction operators, i.e. the operators of nonclassical (or conditional) symmetry of a class of variable coefficient nonlinear wave equations with power nonlinearities is investigated within the framework of singular reduction operator. A…
We give an explicit formula for the wave operators for Schroedinger operators on the half-line with a potential decaying strictly faster than the polynomial of degree minus two. The formula consists of the main term given by the scattering…
We consider the linear problem for water-waves created by sources on the bottom and the free surface in a 3-D basin having slowly varying profile $z=-D(x)$. The fluid verifies Euler-Poisson equations. These (non-linear) equations have been…
A new description for highly nonlinear potential water waves is suggested, where weak 3D effects are included as small corrections to exact 2D equations written in conformal variables. Contrary to the traditional approach, a small parameter…
This paper considers steady surface waves `riding' a Beltrami flow (a three-dimensional flow with parallel velocity and vorticity fields). It is demonstrated that the hydrodynamic problem can be formulated as two equations for two scalar…