4 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…