Takashi Kurose
Fukuoka University
Network
Latest external collaboration on country level. Dive into details by clicking on the dots.
Publication
Featured researches published by Takashi Kurose.
Osaka Journal of Mathematics | 2008
Atsushi Fujioka; Takashi Kurose
We study theory of curves in the complex hyperbola and show that special motions of curves are linked with the Burgers hierarchy, which also leads to a Hamiltonian formulation of the hierarchy and to the difference Burgers equation via their discretization. 1. Introduction It is widely recognized that a lot of differential equations in soliton theory arise from differential geometry especially theory of curves or surfaces ([1, 2, 3]). For example surfaces in the Euclidean 3-space with constant negative Gaussian or non-zero mean curvature are described by the sine or sinh Gordon equation respectively and proper affine spheres are described by the Tzitzeica equatio n. If we refer to theory of curves, the curvature of curves in the Euclidean 2-space evolves according to the mKdV equation under special motions. Pinkall ([4]) showed that the space of closed centroaffine curves in the centroaffine plane possesses a nat ural symplectic structure and the centroaffine curvature evolves according to the KdV e quation when the flow is generated by a Hamiltonian given by the total centroaffine curvature. Chou and Qu ([5, 6]) showed that many soliton equations arise from special motions of plane or space curves. Moreover, Hoffmann and Kutz ([7]) showed that special motions of curves in the complex 1 or 2-space or the complex projective line whose curvature evolves according to the mKdV or KdV equation can be discretized by use of cross ratios. In this paper we study theory of curves in the complex hyperbola which are determined by a certain curvature up to some symmetry. We shall show that special motions of curves are linked with the Burgers hierarchy, which can be formulated as a Hamiltonian system and also leads to the difference Burgers equation ([8]) via their discretization.
International Journal of Geometric Methods in Modern Physics | 2010
Atsushi Fujioka; Takashi Kurose
We study the higher KdV flows on the space of closed complex equicentroaffine curves as Hamiltonian systems. Using a suitable presymplectic structure of the space, we give the Hamiltonian flows associated with the higher KdV equations and a map between the space and the space of closed curves in the complex plane, which induces the Miura transformation between the higher KdV equations and the higher mKdV equations.
Symmetry Integrability and Geometry-methods and Applications | 2014
Atsushi Fujioka; Takashi Kurose
Higher KdV flows on spaces of closed equicentroaffine plane curves are studied and it is shown that the flows are described as certain multi-Hamiltonian systems on the spaces. Multi-Hamiltonian systems describing higher mKdV flows are also given on spaces of closed Euclidean plane curves via the geometric Miura transformation.
Tohoku Mathematical Journal | 1994
Takashi Kurose
Mathematische Zeitschrift | 1990
Takashi Kurose
Interdisciplinary Information Sciences | 2002
Takashi Kurose
Differential Geometry and Its Applications | 2006
Luis J. Alías; Takashi Kurose; Gil Solanes
Journal of The Mathematical Society of Japan | 1989
Takashi Kurose
Kyushu Journal of Mathematics | 2009
Atsushi Fujioka; Takashi Kurose
Results in Mathematics | 1991
Takashi Kurose