7 papers
Modified wave operators for the defocusing cubic nonlinear Schrödinger equation in one space dimension with large scattering data
Masaki Kawamoto, Haruya Mizutani
In the present paper, we construct modified wave operators for the defocusing cubic nonlinear Schrödinger equation (NLS) in one space dimension without size restriction on scatter…
Modified scattering for nonlinear Schrödinger equations with long-range potentials
Masaki Kawamoto, Haruya Mizutani
We study the final state problem for the nonlinear Schrödinger equation with a critical long-range nonlinearity and a long-range linear potential. Given a prescribed asymptotic pr…
Modified scattering for the cubic nonlinear Schrödinger equation with long-range potentials in one space dimension
Masaki Kawamoto, Haruya Mizutani
We consider the cubic nonlinear Schrödinger equation with long-range linear potentials in one space dimension, and prove the modified scattering in the energy space for the associ…
Global Kato smoothing and Strichartz estimates for higher-order Schrödinger operators with rough decay potentials
Haruya Mizutani, Xiaohua Yao
Let \( H = (-Î)^m + V \) be a higher-order elliptic operator on \( L^2(\mathbb{R}^n) \), where \( V \) is a general bounded decaying potential. This paper focuses on the global Ka…
Counterexamples and weak (1,1) estimates of wave operators for fourth-order Schrödinger operators in dimension three
Haruya Mizutani, Zijun Wan, Xiaohua Yao
This paper is dedicated to investigating the -bounds of wave operators associated with fourth-order Schrödinger operators on . We con…
Limiting absorption principle and absence of eigenvalues for massless Klein-Gordon operators on perturbations of the Minkowski spacetime
Haruya Mizutani
We prove a uniform weighted resolvent estimate for the massless Klein-Gordon operator on a curved spacetime which is sufficiently close to the Minkowski spacetime. This particularl…