ﻻ يوجد ملخص باللغة العربية
We analyze the energy transfer for solutions to the defocusing cubic nonlinear Schrodinger (NLS) initial value problem on 2D irrational tori. Moreover we complement the analytic study with numerical experimentation. As a biproduct of our investigation we also prove that the quasi-resonant part of the NLS initial value problem we consider, in both the focusing and defocusing case, is globally well-posed for initial data of finite mass.
We consider a damped/driven nonlinear Schrodinger equation in an $n$-cube $K^{n}subsetmathbb{R}^n$, $n$ is arbitrary, under Dirichlet boundary conditions [ u_t- uDelta u+i|u|^2u=sqrt{ u}eta(t,x),quad xin K^{n},quad u|_{partial K^{n}}=0, quad u>0, ]
An explicit lifespan estimate is presented for the derivative Schrodinger equations with periodic boundary condition.
In this paper we give a new and simplified proof of the theorem on selection of standing waves for small energy solutions of the nonlinear Schrodinger equations (NLS) that we gave in cite{CM15APDE}. We consider a NLS with a Schrodinger operator with
We consider solutions of the defocusing nonlinear Schrodinger (NLS) equation on the half-line whose Dirichlet and Neumann boundary values become periodic for sufficiently large $t$. We prove a theorem which, modulo certain assumptions, characterizes
In this paper we study some key effects of a discontinuous forcing term in a fourth order wave equation on a bounded domain, modeling the adhesion of an elastic beam with a substrate through an elastic-breakable interaction. By using a spectral dec