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pro vyhledávání: '"Mizumachi, Tetsu"'
Autor:
Mizumachi, Tetsu
The KP-II equation was derived by Kadomtsev and Petviashvili to explain stability of line solitary waves of shallow water. Using the Darboux transformations, we study linear stability of 2-line solitons whose line solitons interact elastically each o
Externí odkaz:
http://arxiv.org/abs/2307.09932
Autor:
Mizumachi, Tetsu, Shimabukuro, Yusuke
The $2$D Benney-Luke equation is an isotropic model which describes long water waves of small amplitude in $3$D whereas the KP-II equation is a unidirectional model for long waves with slow variation in the transverse direction. In the case where the
Externí odkaz:
http://arxiv.org/abs/1904.01142
Autor:
Mizumachi, Tetsu
The KP-II equation was derived by [B. B. Kadomtsev and V. I. Petviashvili,Sov. Phys. Dokl. vol.15 (1970), 539-541] to explain stability of line solitary waves of shallow water. Stability of line solitons has been proved by [T. Mizumachi, Mem. of vol.
Externí odkaz:
http://arxiv.org/abs/1808.00809
Autor:
Mizumachi, Tetsu, Shimabukuro, Yusuke
In this paper, we study transverse linear stability of line solitary waves to the $2$-dimensional Benney-Luke equation which arises in the study of small amplitude long water waves in $3$D. In the case where the surface tension is weak or negligible,
Externí odkaz:
http://arxiv.org/abs/1701.03390
Autor:
Mizumachi, Tetsu
The KP-II equation was derived by Kadmotsev and Petviashvili to explain stability of line solitary waves of shallow water. Recently, Mizumachi (Mem. Amer. Math. Soc. 238 (2015)) has proved nonlinear stability of $1$-line solitons for exponentially lo
Externí odkaz:
http://arxiv.org/abs/1512.08334
Autor:
Mizumachi, Tetsu, Tzvetkov, Nikolay
In this article, we will prove $L^2(\mathbb{R})$-stability of $1$-solitons for the KdV equation by using exponential stability property of the semigroup generated by the linearized operator. The proof follows the lines of recent stability argument of
Externí odkaz:
http://arxiv.org/abs/1403.5321
Autor:
Mizumachi, Tetsu
We prove nonlinear stability of line soliton solutions of the KP-II equation with respect to transverse perturbations that are exponentially localized as $x\to\infty$. We find that the amplitude of the line soliton converges to that of the line solit
Externí odkaz:
http://arxiv.org/abs/1303.3532
We study asymptotic stability of solitary wave solutions in the one-dimensional Benney-Luke equation, a formally valid approximation for describing two-way water wave propagation. For this equation, as for the full water wave problem, the classic var
Externí odkaz:
http://arxiv.org/abs/1202.0450
Autor:
Mizumachi, Tetsu, Pelinovsky, Dmitry
Ground states of a L2-subcritical focusing nonlinear Schrodinger (NLS) equation are known to be orbitally stable in the energy class H1 thanks to its variational characterization. In this paper, we will show L2-orbital stability of 1-solitons to a on
Externí odkaz:
http://arxiv.org/abs/1011.5922