ﻻ يوجد ملخص باللغة العربية
We study the inverse problem of recovery a compactly supported non-linearity in the semilinear wave equation $u_{tt}-Delta u+ alpha(x) |u|^2u=0$, in two and three dimensions. We probe the medium with complex-valued harmonic waves of wavelength $h$ and amplitude $h^{-1/2}$, then they propagate in the weakly non-linear regime; and measure the transmitted wave when it exits the support of $alpha$. We show that one can extract the Radon transform of $alpha$ from the phase shift of such waves, and then one can recover $alpha$. We also show that one can probe the medium with real-valued harmonic waves and obtain uniqueness for the linearized problem.
We study the inverse problem of recovery a non-linearity $f(x,u)$, which is compactly supported in $x$, in the semilinear wave equation $u_{tt}-Delta u+ f(x,u)=0$. We probe the medium with either complex or real-valued harmonic waves of wavelength $s
The aim of this paper is to study, in dimensions 2 and 3, the pure-power non-linear Schrodinger equation with an external uniform magnetic field included. In particular, we derive a general criteria on the initial data and the power of the non-linear
We study the problem of unique recovery of a non-smooth one-form $mathcal A$ and a scalar function $q$ from the Dirichlet to Neumann map, $Lambda_{mathcal A,q}$, of a hyperbolic equation on a Riemannian manifold $(M,g)$. We prove uniqueness of the on
We consider the focusing cubic half-wave equation on the real line $$i partial_t u + |D| u = |u|^2 u, widehat{|D|u}(xi)=|xi|hat{u}(xi), (t,x)in Bbb R_+times Bbb R.$$ We construct an asymptotic global-in-time compact two-soliton solution with arbi
We investigate the weakly non-linear evolution of cosmic gravitational clustering in phase space by looking at the Zeldovich solution in the discrete wavelet transform (DWT) representation. We show that if the initial perturbations are Gaussian, the