ﻻ يوجد ملخص باللغة العربية
We continue the study on the transport properties of the Gaussian measures on Sobolev spaces under the dynamics of the cubic fourth order nonlinear Schrodinger equation. By considering the renormalized equation, we extend the quasi-invariance results in [30, 27] to Sobolev spaces of negative regularity. Our proof combines the approach introduced by Planchon, Tzvetkov, and Visciglia [35] with the normal form approach in [30, 27].
We study the wellposedness of Cauchy problem for the fourth order nonlinear Schrodinger equations ipartial_t u=-epsDelta u+Delta^2 u+P((partial_x^alpha u)_{abs{alpha}ls 2}, (partial_x^alpha bar{u})_{abs{alpha}ls 2}),quad tin Real, xinReal^n, where $e
In this paper, we address the long time behaviour of solutions of the stochastic Schrodinger equation in $mathbb{R}^d$. We prove the existence of an invariant measure and establish asymptotic compactness of solutions, implying in particular the existence of an ergodic measure.
We investigate the invariance of the Gibbs measure for the fractional Schrodinger equation of exponential type (expNLS) $ipartial_t u + (-Delta)^{frac{alpha}2} u = 2gammabeta e^{beta|u|^2}u$ on $d$-dimensional compact Riemannian manifolds $mathcal{M}
In this paper, we study the one-dimensional cubic nonlinear Schrodinger equation (NLS) on the circle. In particular, we develop a normal form approach to study NLS in almost critical Fourier-Lebesgue spaces. By applying an infinite iteration of norma
We study the fourth order Schrodinger equation with mixed dispersion on an $N$-dimensional Cartan-Hadamard manifold. At first, we focus on the case of the hyperbolic space. Using the fact that there exists a Fourier transform on this space, we prove