Related papers: Making Waves
Peridynamics describes the nonlinear interactions in spatially extended Hamiltonian systems by nonlocal integro-differential equations, which can be regarded as the natural generalization of lattice models. We prove the existence of…
A discussion is presented, within a simple unifying scheme, about different types of symmetry of PDE's, with the introduction and a precise characterization of the notions of "standard" and "weak" conditional symmetries, together with their…
In the paper, we experimentally study the inverse problem with the resonant scattering determinant. We analyze the structure of characteristics of perturbed linear waves. Assuming there is the common part of potential perturbation…
Diffusion (score-based) generative models have been widely used for modeling various types of complex data, including images, audios, and point clouds. Recently, the deep connection between forward-backward stochastic differential equations…
Motivated by earlier studies of artificial perceptions of light called phosphenes, we analyze traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators modeling this phenomenon. We examine the discrete model…
We construct vector rogue wave solutions of the two-dimensional two coupled nonlinear Schr\"{o}dinger equations with distributed coefficients, namely diffraction, nonlinearity and gain parameters through similarity transformation technique.…
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…
The geometry of impulsive pp-waves is explored via the analysis of the geodesic and geodesic deviation equation using the distributional form of the metric. The geodesic equation involves formally ill-defined products of distributions due…
Variations in distinct restricted spaces of wave functions generate distinct density functionals. In particular, angular momentum projected Slater determinants define a new density functional, compatible simultaneously with angular momentum…
We introduce the notion of tropical Lagrangian multi-sections over a fan and study its relation with toric vector bundles. We also introduce a "SYZ-type" construction for toric vector bundles which gives a reinterpretation of Kaneyama's…
We define and explore the notion of linear weightings for vector bundles, extending the recent work by Loizides and Meinrenken. We construct weighted normal bundles and deformation spaces in the category of vector bundles. We explain how a…
We describe impulsive gravitational pp-waves entirely in the distributional picture. Applying Colombeau's nonlinear framework of generalized functions we handle the formally ill-defined products of distributions which enter the geodesic as…
A Rayleigh wave is a type of surface wave that propagates in the boundary of an elastic solid with traction (or Neumann) boundary conditions. Since the 1980s much work has been done on the problem of constructing a leading term in an…
We study the flow of water waves over bathymetry that varies periodically along one direction. We derive a linearized, homogenized model and show that the periodic bathymetry induces an effective dispersion, distinct from the dispersion…
We consider an extended Korteweg-de Vries (eKdV) equation, the usual Korteweg-de Vries equation with inclusion of an additional cubic nonlinearity. We investigate the statistical behaviour of flat-top solitary waves described by an eKdV…
We derive the exact gravitational wave solutions in a general class of quadratic Poincar\'e gauge gravity models. The Lagrangian includes all possible linear and quadratic invariants constructed from the torsion and the curvature, including…
We study inverse problems consisting on determining medium properties using the responses to probing waves from the machine learning point of view. Based on the understanding of propagation of waves and their nonlinear interactions, we…
A random distribution of poroelastic spheres in a poroelastic medium obeying Biot's theory is considered. The scattering coefficients of the fast and the slow waves are computed in the low frequency limit using the sealed pore boundary…
In this paper we propose the idea of expanding the space of variations in standard variational calculations for the energy by considering the wave function $\psi$ to be a functional of a set of functions $\chi: \psi = \psi[\chi]$, rather…
We study the two-dimensional problem of propagation of linear water waves in deep water in the presence of a submerged body. Under some geometrical requirements, we derive an explicit bound for the solution depending on the domain and the…