[1] The deployment of USArray across the continental U.S. has prompted developments within surface wave tomography to exploit this unprecedented data set. Here, we present a method to measure a new surface wave observable: broadband surface wave amplification that provides new and unique constraints on elastic velocities and density within the crust and upper mantle. The method, similar to its ...

We study the second{order nonlinear damped wave equation semi{discretised in space using standard Galerkin nite element methods. Denoting the analytical solution and the corresponding nite element solution to the given problem by u and u h respectively, we derive an optimal L 2 (() error estimate of the form max t20;T] ku (t) ? u h (t)k C (u) h m ; for (x; t) 2 0; T], where R d ; C is a positiv...

We propose and justify an exponentially convergent algorithm for a second order differential equation with an operator coefficient in Banach space. A particular example of such equation is the strongly damped wave equation arising in viscoelasticity. Numerical examples are given which confirm theoretical results. AMS Subject Classification: 65J10, 65M12, 65M15, 65M06, 65M60, 46N20, 46N40, 47N20...

We consider the damped wave equation αutt +ut = uxx−V ′(u) on the whole real line, where V is a bistable potential. This equation has travelling front solutions of the form u(x, t) = h(x − st) which describe a moving interface between two different steady states of the system, one of which being the global minimum of V . We show that, if the initial data are sufficiently close to the profile of...

In this paper the dynamics of the interaction of attosecond laser pulses with matter is investigated. It will be shown that the master equation: modified Klein-Gordon equation describes the propagation of the heatons. Heatons are the thermal wave packets. When the duration of the laser pulses ∆t is of the order of attosecond the heatonthermal wave packets are nondispersive objects. For ∆t → ∞ t...

A Shallow Water Wave-like nonlinear differential equation is considered by using the generalized bilinear equation with the generalized bilinear derivatives 3,x D and 3,t D , which possesses the same bilinear form as the standard shallow water wave bilinear equation. By symbolic computation, four presented classes of rational solutions contain all rational solutions to the resulting Shallow Wat...

In this paper we present a new highly efficient calculation method for the far field amplitude pattern that arises from scattering problems governed by the d-dimensional Helmholtz equation and, by extension, Schrödinger’s equation. The new technique is based upon a reformulation of the classical real-valued Green’s function integral for the far field amplitude to an equivalent integral over a c...