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pro vyhledávání: '"Tsutsumi, Yoshio"'
Autor:
Kishimoto, Nobu, Tsutsumi, Yoshio
In this article, we consider the kinetic derivative nonlinear Schr\"odinger equation (KDNLS), which is a one-dimensional nonlinear Schr\"odinger equation with a cubic derivative nonlinear term containing the Hilbert transformation. For the Cauchy pro
Externí odkaz:
http://arxiv.org/abs/2303.17360
Autor:
Kishimoto, Nobu, Tsutsumi, Yoshio
We consider the kinetic derivative nonlinear Schr\"odinger equation, which is a one-dimensional nonlinear Schr\"odinger equation with a cubic derivative nonlinear term containing the Hilbert transformation. In our previous work, we proved small-data
Externí odkaz:
http://arxiv.org/abs/2303.17359
We consider the global evolution problem for a model which couples together a nonlinear wave equation and a nonlinear Klein-Gordon equation, and was independently introduced by LeFloch and Y. Ma and by Q. Wang. By revisiting the Hyperboloidal Foliati
Externí odkaz:
http://arxiv.org/abs/2212.12590
Autor:
Kishimoto, Nobu, Tsutsumi, Yoshio
We consider the Cauchy problem for the kinetic derivative nonlinear Schr\"odinger equation on the torus: \[ \partial_t u - i \partial_x^2 u = \alpha \partial_x \big( |u|^2 u \big) + \beta \partial_x \big[ H \big( |u|^2 \big) u \big] , \quad (t, x) \i
Externí odkaz:
http://arxiv.org/abs/2108.13001
Autor:
Debussche, Arnaud, Tsutsumi, Yoshio
We consider the Nonlinear Schr\"odinger (NLS) equation and prove that the Gaussian measure with covariance $(1-\partial_x^2)^{-\alpha}$ on $L^2(\mathbf T)$ is quasi-invariant for the associated flow for $\alpha>1/2$. This is sharp and improves a prev
Externí odkaz:
http://arxiv.org/abs/2002.04899
Akademický článek
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In this paper, we consider the cubic nonlinear Schr\"odinger equation with third order dispersion on the circle. In the non-resonant case, we prove that the mean-zero Gaussian measures on Sobolev spaces $H^s(\mathbb{T})$, $s > \frac 34$, are quasi-in
Externí odkaz:
http://arxiv.org/abs/1805.08409
Autor:
Kishimoto, Nobu, Tsutsumi, Yoshio
We consider the ill-posedness and well-posedness of the Cauchy problem for the third order NLS equation with Raman scattering term on the one dimensional torus. It is regarded as a mathematical model for the photonic crystal fiber oscillator. Regardi
Externí odkaz:
http://arxiv.org/abs/1706.09111
Autor:
Debussche, Arnaud, Tsutsumi, Yoshio
Publikováno v:
In Journal of Functional Analysis 1 August 2021 281(3)
Publikováno v:
In Comptes rendus - Mathématique April 2019 357(4):366-381