In this work we show the existence existence and uniqueness of traveling waves for diffusive-dispersive conservation laws with flux function in C1(R), by using phase plane analysis. Also we estimate the domain of attraction of the equilibrium point attractor corresponding to the right-hand state. The equilibrium point corresponding to the left-hand state is a saddle point. According to the phas...

The main issue in any image zooming techniques is to preserve the structure of the zoomed image. The zoomed image may suffer from the discontinuities in the soft regions and edges; it may contain artifacts, such as image blurring and blocky, and staircase effects. This paper presents a novel image zooming technique using Partial Differential Equations (PDEs). It combines a non-linear Fourth-ord...

Nowadays, options are common financial derivatives. For this reason, by increase of applications for these financial derivatives, the problem of options pricing is one of the most important economic issues. With the development of stochastic models, the need for randomly computational methods caused the generation of a new field called financial engineering. In the financial engineering the pre...

In this article, we consider the Cauchy problem for dispersive equations in α-Modulation spaces. For this purpose, we find a method for estimating uk in α-modulation spaces when k is not an integer, and develop a Strichartz estimate in M p,q which is based on semigroup estimates. In the local case, we that the domain of p is independent of α, which is also the case in the Modulation spaces and ...

We consider the following family of equations: ut = 2uuxxx − uxuxx + 2kuux. Here k 6= 0 is a constant and x ∈ [−L0, L0]. We demonstrate that for these equations: (a) there are compactly supported traveling wave solutions (which are in H) and (b) the Cauchy problem (with H initial data) possesses a weak solution which exists locally in time. These are the the first degenerate dispersive evolutio...

We present a new solution for the dispersive element in astronomical spectrographs, which in many cases can provide an upgrade path to enhance the spectral resolution of existing moderate-resolution reflection-grating spectrographs. We demonstrate that in the case of LRIS-R at the Keck 1 Telescope a spectral resolution of 18,000 can be achieved with reasonable throughput under good seeing condi...

We prove dispersive estimates for solutions to the Schrödinger equation with a real-valued potential V ∈ L∞(R), n ≥ 4, satisfying V (x) = O(〈x〉−(n+2)/2−ǫ), ǫ > 0.