Related papers: A time-domain approach for motion-explicit evaluat…
This paper provides a new analytical method to obtain Green's functions of linear dispersive partial differential equations. The Euler-Bernoulli beam equation and the one-dimensional heat conduction equation (dissipation equation) under…
We compute time-periodic and relative-periodic solutions of the free-surface Euler equations that take the form of overtaking collisions of unidirectional solitary waves of different amplitude on a periodic domain. As a starting guess, we…
The design of structures submitted to aerodynamic loads usually requires the development of specific computational models considering fluid-structure interactions. Models using structural frame elements are developed in several relevant…
The paper introduces a new way to construct dissipative solutions to a second order variational wave equation. By a variable transformation, from the nonlinear PDE one obtains a semilinear hyperbolic system with sources. In contrast with…
The inverse problem is studied in multi-body systems with nonlinear dynamics representing, e.g., phase-locked wave systems, standard multimode and random lasers. Using a general model for four-body interacting complex-valued variables we…
Acoustic fields effect steady transport of suspended particles by rectifying the inertia of primary oscillations. We develop a fully analytic theory that relates this steady particle motion to incident oscillatory (acoustic) flow and the…
Quantum mechanical equations of motion are strictly linear in state descriptors, such as wavefunctions and density matrices, but equations describing chemical kinetics and hydrodynamics may be non-linear in concentrations. This…
Motivated by the viewpoint of integrable systems, we study commuting flows of 2-component quasilinear equations, reducing to investigate the solutions of the wave equation with non-constant speed. In this paper, we apply the reduction…
This paper concerns an inverse elastic scattering problem which is to determine a rigid obstacle from time domain scattered field data for a single incident plane wave. By using Helmholtz decomposition, we reduce the initial-boundary value…
We formulate a depth-averaged non-hydrostatic model to solve wave equations with generation by a moving bottom. This model is built upon the shallow water equations, which are widely used in tsunami wave modelling. An extension leads to two…
By numerical simulation of exact equations of motion (in terms of conformal variables) for planar non-stationary potential flows of an ideal fluid with a free surface over a strongly non-uniform bottom profile, the effect of nonlinear…
We outline a general theory for the analysis of flow-distributed standing and travelling wave patterns in one-dimensional, open plug-flows of oscillatory chemical media. We treat both the amplitude and phase dynamics of small and…
We consider a model of nonlinear wave equations with periodically varying wave speed and periodic external forcing. By imposing non-resonance conditions on the frequency, we establish the existence of the response solutions (i.e., periodic…
An inverse obstacle problem for the wave governed by the wave equation in a two layered medium is considered under the framework of the time domain enclosure method. The wave is generated by an initial data supported on a closed ball in the…
Two-dimensional nonlinear gravity waves travelling in shallow water on a vertically sheared current of constant vorticity are considered. Using Euler equations, in the shallow water approximation, hyperbolic equations for the surface…
The concept of nonlinear modes is useful for the dynamical characterization of nonlinear mechanical systems. While efficient and broadly applicable methods are now available for the computation of nonlinear modes, nonlinear modal testing is…
Two-dimensional free-surface potential flows of an ideal fluid over a strongly inhomogeneous bottom are investigated with the help of conformal mappings. Weakly-nonlinear and exact nonlinear equations of motion are derived by the…
We compute the leading-order inertial corrections to the instantaneous force acting on a rigid body moving with a time-dependent slip velocity in a linear flow field, assuming that the variation of the undisturbed flow at the body scale is…
A challenge in physical oceanography is quantifying the energy content of waves and balanced flows and the fluxes that connect these reservoirs with their sources and sinks. Methodological limitations have prevented decompositions for…
The wave function of a composite system is defined in relativity on a space-time surface. In the explicitly covariant light-front dynamics, reviewed in the present article, the wave functions are defined on the plane $\omega \cd x=0$, where…