Defocusing mKdV flow on centroaffine plane curves

• Park Hyeongki

  Graduate School of Mathematics, Kyushu University

• Kajiwara Kenji

  Institute of Mathematics for Industry, Kyushu University

• Kurose Takashi

  Department of Mathematical Sciences, Kwansei Gakuin University

• Matsuura Nozomu

  Department of Education and Creation Engineering, Kurume Institute of Technology

Abstract

We show that plane curves in the centroaffine geometry admit a flow which is described by the defocusing modified KdV equation. We establish a correspondence between this flow and the KdV flow in the equicentroaffine geometry. We also present an explicit formula for the KdV flow in terms of the $\tau$ function.

Journal

• JSIAM Letters

  JSIAM Letters 10 (0), 25-28, 2018

  The Japan Society for Industrial and Applied Mathematics

Keywords

• defocusing mKdV
• KdV
• centroaffine geometry
• equicentroaffine geometry

Details

• CRID: 1390845712977871616
• NII Article ID: 130007420864
• DOI: 10.14495/jsiaml.10.25
• ISSN: 18830617
• ISSN: 18830609
• Web Site: https://www.jstage.jst.go.jp/article/jsiaml/10/0/10_25/_pdf
• Text Lang: en
• Data Source:
  • JaLC
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed