arXiv subjects

Jumpei Kawakami

Publications and source records attributed to Jumpei Kawakami.

4 recordsLinked to original sources

arXiv2024

Small and large data scattering for the dispersion-managed NLS

We prove several scattering results for dispersion-managed nonlinear Schrödinger equations. In particular, we establish small-data scattering for both `intercritical' and `mass-subcritical' powers by suitable modifications of the standard approach via Strichartz estimates. In addition, we prove scattering for arbitrary data in a weighted Sobolev space for intercritical powers by establishing a pseudoconformal energy estimate. We also rule out (unmodified) scattering for sufficiently low powers. Finally, we give some remarks concerning blowup for the focusing equation.

math.AP↗

arXiv2024

Scattering and blow up for nonlinear Schrödinger equation with the averaged nonlinearity

We consider the 3-dimensional nonlinear Schrödinger equation (NLS) with average nonlinearity. This is a limiting model of NLS with strong magnetic confinement and a generalized model of the resonant system of NLS with a partial harmonic oscillator in terms of nonlinear power. We provide a new proof for the conservation law of kinetic energy and remove the restriction on nonlinearity. Moreover, in the case of focusing, super-quintic, and sub-nonic, we construct a new ground-state solution and classify the behavior of the solutions below the ground state. We demonstrate a sharp threshold for scattering and blow-up.

math.AP↗

arXiv2023

Averaging of strong magnetic nonlinear Schrödinger equations in the energy space

In this study, we consider two nonlinear Schrödinger-type models that are derived by R L. Frank, F. Méhats, C. Sparber [arXiv:1611.01574] to study 3D nonlinear Schrödinger equations under strong magnetic fields. One model is derived by spatial scaling and the other is obtained by averaging the spatial scaled model over time. We study these models in the energy space to obtain global solutions and improve the convergence result over an arbitrarily long time. Regarding the nonic nonlinear power of the time averaged model, we prove a scattering result under a scaling-invariant small-energy condition, which underlines energy-criticality of the nonic case.

math.AP↗

arXiv2023

Global approximation for the cubic NLS with strong magnetic confinement

We consider nonlinear Schrödinger equation with strong magnetic fields in 3D. This model was derived by R L. Frank, F. Méhats, C. Sparber in 2017. We prove modified scattering for small initial data and the existence of modified wave operator for small final data. To describe asymptotic behavior of the NLS we use the time-averaged model which was derived by the same authors as "the strong magnetic confinement limit" of the NLS. We construct asymptotic solutions which satisfy both asymptotic in time evolution and convergence in the strong magnetic confinement limit. We also analyze the error between the solution to the NLS and the time-averaged model for the same initial data and obtain global estimates.

math.AP↗