42 citations · 80 across the 9 of their papers we have counts for
7 papers · 1 filter
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…
Asymptotic Linear Stability of the Benney-Luke equation in 2D
Tetsu Mizumachi, Yusuke Shimabukuro
In this paper, we study transverse linear stability of line solitary waves to the -dimensional Benney-Luke equation which arises in the study of small amplitude long water waves…
Global solution of the Wadati-Konno-Ichikawa equation with small initial data
Yusuke Shimabukuro
We show the existence of global solution for the Wadati-Konno-Ichikawa (WKI) equation with small initial data in the smooth function space. Our approach is based on the scattering…
Existence of global solutions to the derivative NLS equation with the inverse scattering transform method
Dmitry E. Pelinovsky, Yusuke Shimabukuro
We address existence of global solutions to the derivative nonlinear Schrödinger (DNLS) equation without the small-norm assumption. By using the inverse scattering transform method…
Transverse instability of line solitons in massive Dirac equations
Dmitry Pelinovsky, Yusuke Shimabukuro
Working in the context of localized modes in periodic potentials, we consider two systems of the massive Dirac equations in two spatial dimensions. The first system, a generalized…
orbital stability of Dirac solitons in the massive Thirring model
Andres Contreras, Dmitry E. Pelinovsky, Yusuke Shimabukuro
We prove orbital stability of Dirac solitons in the massive Thirring model. Our analysis uses local well posedness of the massive Thirring model in , conservation of the…
Orbital stability of Dirac solitons
Dmitry E. Pelinovsky, Yusuke Shimabukuro
We prove orbital stability of Dirac solitons in the integrable massive Thirring model by working with an additional conserved quantity which complements Hamiltonian, momentum…