ﻻ يوجد ملخص باللغة العربية
We consider a nonlinear Klein Gordon equation (NLKG) with short range potential with eigenvalues and show that in the contest of complex valued solutions the small standing waves are attractors for small solutions of the NLKG. This extends the results already known for the nonlinear Schrodinger equation and for the nonlinear Dirac equation. In addition, this extends a result of Bambusi and Cuccagna (which in turn was an extension of a result by Soffer and Weinstein) which considered only real valued solutions of the NLKG.
Joining together virial inequalities by Kowalczyk, Martel and Munoz and Kowalczyk, Martel, Munoz and Van Den Bosch with our theory on how to derive nonlinear induced dissipation on discrete modes, and in particular the notion of Refined Profile, we s
We consider a Nonlinear Schrodinger Equation with a very general non linear term and with a trapping $delta $ potential on the line. We then discuss the asymptotic behavior of all its small solutions, generalizing a recent result by Masaki et al. We
We study the long time behavior of small (in $l^2$) solutions of discrete nonlinear Schrodinger equations with potential. In particular, we are interested in the case that the corresponding discrete Schrodinger operator has exactly two eigenvalues. W
We study the interaction of a ground state with a class of trapping potentials. We track the precise asymptotic behavior of the solution if the interaction is weak, either because the ground state moves away from the potential or is very fast.
We prove scattering for the radial nonlinear Klein-Gordon equation $ partial_{tt} u - Delta u + u = -|u|^{p-1} u $ with $5 > p >3$ and data $ (u_{0}, u_{1}) in H^{s} times H^{s-1} $, $ 1 > s > 1- frac{(5-p)(p-3)}{2(p-1)(p-2)} $ if $ 4 geq p > 3 $ and