26 citations · 56 across the 10 of their papers we have counts for
10 papers
The evolution of a curve induced by the Pohlmeyer-Lund-Regge equation
Shimpei Kobayashi, Yuhei Kogo, Nozomu Matsuura
This paper investigates the evolution of space curves governed by the Pohlmeyer-Lund-Regge (PLR) equation, an integrable extension of the sine-Gordon equation. We examine a specifi…
Curvature surfaces in generic conformally flat hypersurfaces arising from Poincaré metric -- Extension and Approximation
Nozomu Matsuura, Yoshihiko Suyama
We study generic conformally flat (analytic-)hypersurfaces in the Euclidean -space . Such a local-hypersurface is obtained as an evolution of surfaces issuing from…
Representation formula for discrete indefinite affine spheres
Shimpei Kobayashi, Nozomu Matsuura
We present a representation formula for discrete indefinite affine spheres via loop group factorizations. This formula is derived from the Birkhoff decomposition of loop groups ass…
Isoperimetric deformations of curves on the Minkowski plane
Hyeongki Park, Jun-ichi Inoguchi, Kenji Kajiwara +3
We formulate an isoperimetric deformation of curves on the Minkowski plane, which is governed by the defocusing mKdV equation. Two classes of exact solutions to the defocusing mKdV…
Discrete Local Induction Equation
Sampei Hirose, Jun-ichi Inoguchi, Kenji Kajiwara +2
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 co…
dNLS Flow on Discrete Space Curves
Sampei Hirose, Jun-ichi Inoguchi, Kenji Kajiwara +2
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 co…
Isogonal Deformation of Discrete Plane Curves and Discrete Burgers Hierarchy
Kenji Kajiwara, Toshinobu Kuroda, Nozomu Matsuura
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, w…
Discrete mKdV and Discrete Sine-Gordon Flows on Discrete Space Curves
Jun-ichi Inoguchi, Kenji Kajiwara, Nozomu Matsuura +1
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 sho…
Explicit solutions to the semi-discrete modified KdV equation and motion of discrete plane curves
Jun-ichi Inoguchi, Kenji Kajiwara, Nozomu Matsuura +1
We construct explicit solutions to continuous motion of discrete plane curves described by a semi-discrete potential modified KdV equation. Explicit formulas in terms the funct…
Motion and Bäcklund Transformations of Discrete Plane Curves
Jun-ichi Inoguchi, Kenji Kajiwara, Nozomu Matsuura +1
We construct explicit solutions to the discrete motion of discrete plane curves that has been introduced by one of the authors recently. Explicit formulas in terms the function…