We propose and analyze a fast method for computing the solution of the high frequency Helmholtz equation in a bounded one-dimensional domain with a variable wave speed function. The method is based on wave splitting. The Helmholtz equation is split into one–way wave equations with source functions which are solved iteratively for a given tolerance. The source functions depend on the wave speed ...

In this paper, we propose the extended Boussinesq–Whitham–Broer–Kaup (BWBK)-type equations with variable coefficients and fractional order. We consider BWBK equations, Whitham–Broer–Kaup (WBK) Boussinesq by setting proper smooth functions that are derived from proposed equation. obtain uniformly coupled traveling wave solutions of considered employing improved system method, subsequently their ...

In this thesis, we propose and analyze a fast method for computing the solution of the Helmholtz equation in a bounded domain with a variable wave speed function. The method is based on wave splitting. The Helmholtz equation is first split into one–way wave equations which are then solved iteratively for a given tolerance. The source functions depend on the wave speed function and on the soluti...

In this article we consider variable coefficient time dependent wave equations in R×R. Using phase space methods we construct outgoing parametrices and prove Strichartz type estimates globally in time. This is done in the context of C metrics which satisfy a weak asymptotic flatness condition at infinity.

in this work, we analyse a pair of two-dimensional coupled reaction-diusion equations known as the gray-scott model, in which spot patterns have been observed. we focus on stationary patterns, and begin by deriving the asymptotic scaling of the parameters and variables necessary for the analysis of these patterns. a complete bifurcation study of these solutions is presented. the main mathematic...

The problem of propagation of plane wave including body and surface waves propagating in a transversely isotropic half-space with a depth-wise axis of material symmetry is investigated in details. Using the advantage of representation of displacement fields in terms of two complete scalar potential functions, the coupled equations of motion are uncoupled and reduced to two independent equations...

differential transform method has been applied to solve many functional equations so far. in this article, we have used this method to solve wave-like equations. differential transform method is capable of reducing the size of computational work. exact solutions can also be achieved by the known forms of the series solutions. some examples are prepared to show theefficiency and simplicity of th...