89 citations · 190 across the 20 of their papers we have counts for
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Spectral stability of resonant Y-solitons for the KP-II equation
Tetsu Mizumachi
The KP-II equation was introduced by Kadomtsev and Petviashvili to explain the transverse stability of line solitary waves in shallow water. Using Darboux transformations, we prove…
A note on the non-existence of small non-trivial compact solutions for Euler-Poisson equation in 1D
Masaya Maeda, Tetsu Mizumachi
In this short note, we prove the non-existence of slow and fast small nontrivial compact solutions for the Euler-Poisson system in D. The proof is based on the virial estimate w…
Transverse linear stability of line solitons for 2D Toda
Tetsu Mizumachi
The -dimensional Toda lattice (D Toda) is a completely integrable semi-discrete wave equation with the KP-II equation in its continuous limit. Using Darboux transformations,…
Linear stability of elastic 2-line solitons for the KP-II equation
Tetsu Mizumachi
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 stabil…
Stability of Benney-Luke line solitary waves in 2D
Tetsu Mizumachi, Yusuke Shimabukuro
The D Benney-Luke equation is an isotropic model which describes long water waves of small amplitude in D whereas the KP-II equation is a unidirectional model for long waves…
The phase shift of line solitons for the KP-II equation
Tetsu Mizumachi
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. Sta…