Kenji Kajiwara, Toshinobu Kuroda and Nozomu Matsuura
Pacific Journal of Mathematics for Industry 8(1) 1-14 Mar 2016 [Refereed]
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...
Kenji Kajiwara, Masatoshi Noumi and Yasuhiko Yamada
J. Phys. A: Math. Theoret. 50(7) 073001 Jan 2017 [Refereed]
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 ...
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...
International Mathematical Research Notices Nov 2013 [Refereed]
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 Oct 2013 [Refereed]
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.
Comment. Math. Univ. St. Pauli 64 29-45 May 2015 [Refereed]
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...
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 Sep 2013 [Refereed]
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.
We consider an integrability test for ultradiscrete equations based on the
singularity confinement analysis for discrete equations. We show how
singularity pattern of the test is transformed into that of ultradiscrete
equation. The ultradiscrete s...
Kenji Kajiwara, Yasuhiro Ohta, Junkichi Satsuma, Basil Grammaticos, Alfred Ramani
We present a class of solutions to the discrete Painlevé-II equation for
particular values of its parameters. It is shown that these solutions can be
expressed in terms of Casorati determinants whose entries are discrete Airy
functions. The anal...
Development and Extension of Integrable Discrete Differential Geometry
JSPS: KAKENHI (Scientific Research (B))
Project Year: Apr 2016 - Mar 2020 Investigator(s): Kenji Kajiwara
Construction of Discrete-time Geometric Models Based on Discrete Differential Geometry
JSPS: KAKENHI (Challenging Exploratory Research)
Project Year: Apr 2016 - Mar 2018 Investigator(s): Kenji Kajiwara
Modeling for CG based on discrete integrable systems
Kobe Studio Seminar:
Project Year: Jan 2016 Investigator(s): Kenji Kajiwara
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...