ﻻ يوجد ملخص باللغة العربية
We investigate the stability of ground states to a nonlinear focusing Schrodinger equation in presence of a Kirchhoff term. Through a spectral analysis of the linearized operator about ground states, we show a modulation stability estimate of ground states in the spirit of one due to Weinstein [{it SIAM J. Math. Anal.}, 16(1985),472-491].
We give short survey on the question of asymptotic stability of ground states of nonlinear Schrodinger equations, focusing primarily on the so called nonlinear Fermi Golden Rule.
We study the existence of ground states to a nonlinear fractional Kirchhoff equation with an external potential $V$. Under suitable assumptions on $V$, using the monotonicity trick and the profile decomposition, we prove the existence of ground state
This paper is concerned with the existence of ground states for a class of Kirchhoff type equation with combined power nonlinearities begin{equation*} -left(a+bint_{mathbb{R}^{3}}| abla u(x)|^{2}right) Delta u =lambda u+|u|^{p-2}u+u^{5}quad text{for
In this paper, we study the existence and instability of standing waves with a prescribed $L^2$-norm for the fractional Schr{o}dinger equation begin{equation} ipartial_{t}psi=(-Delta)^{s}psi-f(psi), qquad (0.1)end{equation} where $0<s<1$, $f(psi)=|ps
We prove nonlinear modulational instability for both periodic and localized perturbations of periodic traveling waves for several dispersive PDEs, including the KDV type equations (e.g. the Whitham equation, the generalized KDV equation, the Benjamin