HAMILTONIAN FORMALISM FOR THE HIGHER KdV FLOWS ON THE SPACE OF CLOSED COMPLEX EQUICENTROAFFINE CURVES

DOI10.1142/S0219887810003987zbMath1203.53010MaRDI QIDQ5306184

Takashi Kurose, Atsushi Fujioka

Publication date: 8 April 2010

Published in: International Journal of Geometric Methods in Modern Physics (Search for Journal in Brave)

zbMATH Keywords

evolution equationsKdV equationHamiltonian systemaffine differential geometrycurve theory

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Affine differential geometry (53A15) Correspondences and other transformation methods (e.g., Lie-Bäcklund) for PDEs on manifolds (58J72)

Related Items (6)

Self-Bäcklund curves in centroaffine geometry and Lamé’s equation ⋮ Central affine curve flow on the plane ⋮ On centro-affine curves and Bäcklund transformations of the KdV equation ⋮ Isoperimetric deformations of curves on the Minkowski plane ⋮ ON THE GEOMETRY OF STAR-SHAPED CURVES IN R<i>ⁿ</i> ⋮ Defocusing mKdV flow on centroaffine plane curves

Cites Work

• Remarks on KdV-type flows on star-shaped curves
• Lie groups and KdV equations
• Integrable motions of space curves in affine geometry
• Hamiltonian flows on the space of star-shaped curves
• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
• Korteweg-de Vries Equation and Generalizations. II. Existence of Conservation Laws and Constants of Motion
• Korteweg-deVries Equation and Generalizations. V. Uniqueness and Nonexistence of Polynomial Conservation Laws
• GEOMETRY OF THE SPACE OF CLOSED CURVES IN THE COMPLEX HYPERBOLA
• Integrals of nonlinear equations of evolution and solitary waves
• Integrable equations arising from motions of plane curves

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