We consider the cubic nonlinear Schrödinger equation posed on the spatial domain R× Td.
We prove modified scattering and construct modified wave operators for small initial and …

We consider the Schrödinger equation with no radial assumption on real hyperbolic spaces
Hn. We obtain in all dimensions n⩾ 2 sharp dispersive and Strichartz estimates for a large …

In this paper we present a method to study global regularity properties of solutions of large-
data critical Schrödinger equations on certain noncompact Riemannian manifolds. We rely …

In this paper, we study the (pointwise) decaying property of quintic NLS on the three-
dimensional hyperbolic space H 3. We show the nonlinear solution enjoys the same decay …

Abstract In Do, Doi proved that the L^ 2 _ t H^ 1/2 _ x local smoothing effect for Schrödinger
equations on a Riemannian manifold does not hold if the geodesic flow has one trapped …

Abstract We consider the Klein–Gordon equation associated with the Laplace–Beltrami
operator Δ on real hyperbolic spaces of dimension n≥ 2; as Δ has a spectral gap, the wave …

In this article, global-in-time dispersive estimates and Strichartz estimates are explored for
the wave equation on three dimensional hyperbolic space. Due to the negative curvature …

We consider the mass-critical focusing nonlinear Schrödinger equation in the presence of
an external potential, when the nonlinearity is inhomogeneous. We show that if the …

Let $\Delta $ be the Laplace-Beltrami operator on a non-compact symmetric space of any
rank, and denote the bottom of its $ L^ 2$-spectrum as $-|\rho|^{2} $. In this paper, we …

We consider the generalized Boussinesq (GBq) equation on the real hyperbolic space
$\mathbb {H}^{n} $($ n\geq2 $) in a rough framework based on Lorentz spaces. First, we …