arXiv subjects

Kazuki Aoki

Publications and source records attributed to Kazuki Aoki.

3 recordsLinked to original sources

arXiv2021

Modified scattering for inhomogeneous nonlinear Schrödinger equations with and without inverse-square potential

We consider the final state problem for the inhomogeneous nonlinear Schrödinger equation with a critical long-range nonlinearity. Given a prescribed asymptotic profile, which has a logarithmic phase correction compared with the free evolution, we construct a unique global solution which converges to the profile. As a consequence, the existence of modified wave operators for localized small scattering data is obtained. We also study the same problem for the case with the critical inverse-square potential under the radial symmetry. In particular, we construct the modified wave operators for the long-range nonlinear Schrödinger equation with the critical inverse-square potential in three space dimensions, under the radial symmetry.

math.AP↗

arXiv2020

Asymptotic behavior for the long-range nonlinear Schrödinger equation on star graph with the Kirchhoff boundary condition

We consider the cubic nonlinear Schrödinger equation on the star graph with the Kirchhoff boundary condition. We prove modified scattering for the final state problem and the initial value problem. Moreover, we also consider the failure of scattering for the Schrödinger equation with power-type long-range nonlinearities. These results are extension of the results for NLS on the one dimensional Euclidean space.

math.AP↗

arXiv2019

Failure of scattering to standing waves for a Schrödinger equation with long-range nonlinearity on star graph

We consider the Schrödinger equation with power type long-range nonlinearity on star graph. Under a general boundary condition at the vertex, including Kirchhoff, Dirichlet, $δ$, or $δ'$ boundary condition, we show that the non-trivial global solution does not scatter to standing waves. Our proof is based on the argument by Murphy and Nakanishi, who treated the long-range nonlinear Schrödinger equation with a general potential in the Euclidean space, in order to consider general boundary conditions.

math.AP↗