The benefit of finding particular exact and asymptotic solutions of non-integrable non-linear partial differential equations is considered. It is shown how explicit analytical solutions predict important features of the waves behavior even outside their formal applicability. In particular, an arbitrary initial pulse splits in a numerical solution into the train of localized waves each described...

This paper presents an overview of the acoustic wave equation and the common time-domain numerical solution strategies in closed environments. First, the wave equation is presented and its qualities analyzed. Common principles of numerical approximation of derivatives are then reviewed. Based on them, the finite difference (FD) and the finite element methods (FEM) for the solution of the wave e...

We consider the homogenization of the wave equation with high frequency initial conditions propagating in a medium with highly oscillatory random coefficients. By appropriate mixing assumptions on the random medium, we obtain an error estimate between the exact wave solution and the homogenized wave solution in the energy norm. This allows us to consider the limiting behavior of the energy dens...

The power law wave equation uses two different fractional derivative terms to model wave propagation with power law attenuation. This equation averages complex nonlinear dynamics into a convenient, tractable form with an explicit analytical solution. This paper develops a random walk model to explain the appearance and meaning of the fractional derivative terms in that equation, and discusses a...

Algebro-geometric solution is a kind of very important solution in the integrable system. The soliton solution, breather solution and rogue wave solution can be obtained from the algebrogeometric solution through special limit. Therefore, we agree that almost all the “new soliton solutions” of the vector NLS equation are contained in the general formula in [1] as particular cases. However, it i...

it is over several decades that ultrasound is used to enhance the transdermal drug delivery (phonphoresis). the mechanism of the enhancement is not fully understood and the ability of ultrasound on the enhancement for some drugs is unclear. the effect of continuous wave 870 khz ultrasound at intensity of 1 w/cm 2 for 15 minutes on transdermal absorption of piroxicam from solution and gel formul...