Kenji Kajiwara, Masatoshi Noumi and Yasuhiko Yamada
J. Phys. A: Math. Theoret. 50(7) 073001 2017年1月 [査読有り]
In this paper a comprehensive review is given on the current status of
achievements in the geometric aspects of the Painlevé equations, with a
particular emphasis on the discrete Painlevé equations. The theory is
controlled by the geometry of ...
Kenji Kajiwara, Toshinobu Kuroda and Nozomu Matsuura
Pacific Journal of Mathematics for Industry 8(1) 1-14 2016年3月 [査読有り]
We study deformations of plane curves in the similarity geometry. It is known that continuous deformations of smooth curves are described by the Burgers hierarchy. In this paper, we formulate the discrete deformation of discrete plane curves descr...
The local induction equation, or the binormal flow on space curves is a well-known model of deformation of space curves as it describes the dynamics of vortex filaments, and the complex curvature is governed by the nonlinear Schödinger equation (N...
Comment. Math. Univ. St. Pauli 64 29-45 2015年5月 [査読有り]
A relation between the Goldstein-Petrich hierarchy for plane curves and the Toda lattice hierarchy is investigated. A representation formula for plane curves is given in terms of a special class of τ-functions of the Toda lattice hierarchy. A repr...
In this paper, we consider the discrete deformation of the discrete space curves with constant torsion described by the discrete mKdV or the discrete sine-Gordon equations, and show that it is formulated as the torsion-preserving equidistant defor...
Hisashi Ando, Mike Hay, Kenji Kajiwara, Tetsu Masuda
Funkcialaj Ekvacioj 57(1) 1-41 2014年4月 [査読有り]
We present an explicit formula for the discrete power function introduced by
Bobenko, which is expressed in terms of the hypergeometric functions for
the sixth Painlevé equation. The original definition of the discrete power
International Mathematical Research Notices 2013年11月 [査読有り]
We consider the symmetric q-Painlevé equations derived from the birational representation of affine Weyl groups by applying the projective reduction and construct the hypergeometric solutions. Moreover, we discuss continuous limits of the symmetr...
B.F. Feng, J. Inoguchi, K. Kajiwara, K. Maruno, Y. Ohta
Frontiers of Mathematics in China Frontiers of Mathematics in China 8(5) 1017-1029 2013年10月 [査読有り]
Integrable discretizations of the complex and real Dym equations are proposed. N-soliton solutions for both semi-discrete and fully discrete analogues of the complex and real Dym equations are also presented.
Semi-discrete analogues of the elastic beam equation and the short pulse equation
K. Maruno, B.F. Feng, J. Inoguchi, K. Kajiwara, Y. Ohta
Proceedings of 2013 International Symposium on Nonlinear Theory and its Applications 278-281 2013年9月 [査読有り]
Two integrable nonlinear differential- difference systems, semi-discrete analogues of the Wadati-Konno-Ichikawa elastic beam equation and the short pulse equation, are constructed by using a geometric approach.
Modeling for CG based on discrete integrable systems
Kobe Studio Seminar:
研究期間: 2016年1月 代表者: 梶原健司
The purpose of this project is to develop modelling technique for computer graphics based on
discrete integrable systems. The theory of discrete integrable systems provides skeletons of
dynamics of geometric objects such as discrete curves and di...