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pro vyhledávání: '"HIRAYAMA, HIROYUKI"'
We consider the Cauchy problem of a system of quadratic derivative nonlinear Schr\"odinger equations which was introduced by M. Colin and T. Colin (2004) as a model of laser-plasma interaction. For the nonperiodic setting, the authors proved some wel
Externí odkaz:
http://arxiv.org/abs/2407.03565
Autor:
Hirayama, Hiroyuki, Oka, Yasuyuki
Publikováno v:
J. Differential Equations 412 (2024), 214-249
The aim of this paper is to give existence and uniqueness results for solutions of the Cauchy problem for semilinear heat equations on stratified Lie groups $\mathbb{G}$ with the homogeneous dimension $N$. We consider the nonlinear function behaves l
Externí odkaz:
http://arxiv.org/abs/2404.03128
Autor:
Fukuda, Ikki, Hirayama, Hiroyuki
Publikováno v:
Nonlinear Anal. Real World Appl. 79 (2024), Paper No. 104130, 30 pp
We consider the Cauchy problem for the generalized Zakharov-Kuznetsov-Burgers equation in 2D. This is one of the nonlinear dispersive-dissipative equations, which has a spatial anisotropic dissipative term $-\mu u_{xx}$. In this paper, we prove that
Externí odkaz:
http://arxiv.org/abs/2311.12374
Autor:
Hirayama, Hiroyuki, Ikeda, Masahiro
We consider the Cauchy problem of the system of nonlinear Schr\"odinger equations with derivative nonlinearlity. This system was introduced by Colin-Colin (2004) as a model of laser-plasma interactions. We study existence of ground state solutions an
Externí odkaz:
http://arxiv.org/abs/2307.00980
This paper is concerned with the Cauchy problem of the quadratic nonlinear Schr\"{o}dinger equation in $\mathbb{R} \times \mathbb{R}^2$ with the nonlinearity $\eta |u|^2$ where $\eta \in \mathbb{C} \setminus \{0\}$ and low regularity initial data. If
Externí odkaz:
http://arxiv.org/abs/2209.12176
Autor:
Fukuda, Ikki, Hirayama, Hiroyuki
Publikováno v:
Nonlinear Anal. 234 (2023), Paper No. 113322, 24 pp
We consider the Cauchy problem for the generalized Kadomtsev--Petviashvili--Burgers equation in 2D. This is one of the nonlinear dispersive-dissipative type equations, which has a spatial anisotropic dissipative term. Under some suitable regularity a
Externí odkaz:
http://arxiv.org/abs/2208.11379
Autor:
Fukuda, Ikki, Hirayama, Hiroyuki
Publikováno v:
In Nonlinear Analysis: Real World Applications October 2024 79
Publikováno v:
In Journal of Differential Equations 25 June 2024 395:181-222
Publikováno v:
J. Math. Anal. Appl. 499 (2021), no. 2, Paper No. 125028, 29 pp
In this paper, we consider the Cauchy problem of the system of quadratic derivative nonlinear Schr\"odinger equations introduced by Colin and Colin (2004). We determine an almost optimal Sobolev regularity where the smooth flow map of the Cauchy prob
Externí odkaz:
http://arxiv.org/abs/2009.13072
Publikováno v:
NoDEA Nonlinear Differential Equations Appl. 28 (2021), no. 5, Paper No. 46, 72 pp
We study the Cauchy problem to the semilinear fourth-order Schr\"odinger equations: \begin{equation}\label{0-1}\tag{4NLS} \begin{cases} i\partial_t u+\partial_x^4u=G\left(\left\{\partial_x^{k}u\right\}_{k\le \gamma},\left\{\partial_x^{k}\bar{u}\right
Externí odkaz:
http://arxiv.org/abs/2004.03215