Zobrazeno 1 - 10
of 87
pro vyhledávání: '"Miyazaki, Hayato"'
In this paper, we consider the nonlinear Schr\"{o}dinger equation with a general homogeneous nonlinearity in dimensions up to three. We assume that the degree (i.e., power) of the nonlinearity is such that the equation is mass-subcritical and short-r
Externí odkaz:
http://arxiv.org/abs/2409.08432
Autor:
Kawamoto, Masaki, Miyazaki, Hayato
This paper is concerned with nonlinear Schr\"odinger equations with a time-decaying harmonic potential. The nonlinearity is gauge-invariant of the long-range critical order. In [24] and [22], it is proved that the equation admits a nontrivial solutio
Externí odkaz:
http://arxiv.org/abs/2403.02657
Autor:
Kawamoto, Masaki, Miyazaki, Hayato
Publikováno v:
Journal of Differential Equations 365 (2023) 127-167
This paper is concerned with the final state problem for the homogeneous type nonlinear Schr\"odinger equation with time-decaying harmonic potential. The nonlinearity has the critical order and is not necessarily the form of a polynomial. In the case
Externí odkaz:
http://arxiv.org/abs/2206.08168
We consider the final state problem for the inhomogeneous nonlinear Schr\"odinger equation with a critical long-range nonlinearity. Given a prescribed asymptotic profile, which has a logarithmic phase correction compared with the free evolution, we c
Externí odkaz:
http://arxiv.org/abs/2101.09423
Publikováno v:
Pure Appl. Analysis 4 (2022) 287-311
We consider the cubic nonlinear Schr\"{o}dinger 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 scatte
Externí odkaz:
http://arxiv.org/abs/2006.13490
Autor:
Miyazaki, Hayato, Sobajima, Motohiro
Publikováno v:
Advances in Harmonic Analysis and Partial Differential Equations (2020), pp. 197-207
This paper is concerned with the upper bound of the lifespan of solutions to nonlinear Schr\"odinger equations with general homogeneous nonlinearity of the critical order. In [8], Masaki and the first author obtain the upper bound of the lifespan of
Externí odkaz:
http://arxiv.org/abs/1912.12794
Autor:
Miyazaki, Hayato
Publikováno v:
Discrete Contin. Dyn. Syst. 41 (2021), no. 5, 2411-2445
This paper is concerned with strong blow-up instability (Definition 1.3) for standing wave solutions to the system of the quadratic nonlinear Klein-Gordon equations. In the single case, namely the nonlinear Klein-Gordon equation with power type nonli
Externí odkaz:
http://arxiv.org/abs/1911.08157
Autor:
Kawamoto, Masaki, Miyazaki, Hayato
Publikováno v:
In Journal of Differential Equations 25 August 2023 365:127-167
Autor:
Miyazaki, Hayato
This paper is concerned with the local well-posedness for the higher-order generalized KdV type equation with low-degree of nonlinearity. The equation arises as a non-integrable and lower nonlinearity version of the higher-order KdV equation. As for
Externí odkaz:
http://arxiv.org/abs/1903.04142
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