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.

We prove dispersive estimates at low frequency in dimensions n ≥ 4 for the wave equation for a very large class of real-valued potentials, provided the zero is neither an eigenvalue nor a resonance. This class includes potentials V ∈ L∞(R) satisfying V (x) = O ( 〈x〉−(n+1)/2−ǫ ) , ǫ > 0.

We estimate the di-photon coupling of f0(600), f0(980) and f2(1270) resonances in a couple channel dispersive approach. Especially we estimate the di-photon coupling of the third sheet pole located near K̄K threshold, denoted as f III 0 (980). It is argued that this third sheet pole may be originated from a couple channel Breit-Wigner description of the f0(980) resonance. The f0(600) di-photon c...

Article history: Received 11 October 2013 Received in revised form 14 July 2014 Accepted 19 August 2014 Available online 28 August 2014

in this paper, we obtain a suitable mathematical model for the seismic response of dams. by using the shear beam model (sb model), we give a mathematical formulation that it is a partial differential equation and transform it to the sturm-liouville equation.

The L-theory of solutions of the homogeneous A-harmonic equation d A x, dω 0 for differential forms has been very well developed in recent years. Many L-norm estimates and inequalities, including the Hardy-Littlewood inequalities, Poincaré inequalities, Caccioppoli-type estimates, and Sobolev imbedding inequalities, for solutions of the homogeneous A-harmonic equation have been established; see...