A general symmetric Trefftz Discontinuous Galerkin method is built for solving the Helmholtz equation with piecewise constant coefficients. The construction of the corresponding local solutions to the Helmholtz equation is based on a boundary element method. A series of numerical experiments displays an excellent stability of the method relatively to the penalty parameters, and more importantly...

The properties of the so-called regularized short pulse equation (RSPE) are explored with a particular focus on the traveling wave solutions of this model. We theoretically analyze and numerically evolve two sets of such solutions. First, using a fixed point iteration scheme, we numerically integrate the equation to find solitary waves. It is found that these solutions are well approximated by ...

Two ultracold atoms moving in a trap interact weakly at a very short distance. This interaction can be modeled by a properly regularized contact potential. We solve the corresponding time{independent Schrr odinger equation under the assumption of a parabolic, spherically symmetric trapping potential.

This paper studies axially symmetric vibrations of a liquid-filled poroelastic thin cylinder saturated with two immiscible liquids of infinite extent that is surrounded by an inviscid elastic liquid. By considering the stress free boundaries, the frequency equation is obtained. Particular case, namely, liquid-filled poroelastic cylinder saturated with single liquid is discussed.  When the waven...

We consider a second-order nonlinear wave equation with linear convolution term. When the operator is taken as identity operator, our reduces to classical elasticity which can be written $p$-system of first-order differential equations. first establish local well-posedness Cauchy problem. then investigate behavior solutions problem in limit kernel function integral approaches Dirac delta functi...