GEOMETRIC KdV FLOWS, MOTIONS OF CURVES AND THE THIRD-ORDER SYSTEM OF THE AKNS HIERARCHY

DOI10.1142/S0129167X11007100zbMath1228.37048OpenAlexW2116043427MaRDI QIDQ3094369

Qing Ding, You-De Wang

Publication date: 24 October 2011

Published in: International Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0129167x11007100

zbMATH Keywords

equivalencepara-Kähler structureKdV flowcurve flow

Mathematics Subject Classification ID

Symplectic manifolds (general theory) (53D05) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry (37K25)

Related Items (7)

Geometric Schrödinger-Airy flows on Kähler manifolds ⋮ The almost complex structure on 𝕊6 and related Schrödinger flows ⋮ The noncommutative KdV equation and its para-Kähler structure ⋮ New geometric flows on Riemannian manifolds and applications to Schrödinger-Airy flows ⋮ Vortex filament on symmetric Lie algebras and generalized bi-Schrödinger flows ⋮ On the vortex filament in 3-spaces and its generalizations ⋮ Local existence of a fourth-order dispersive curve flow on locally Hermitian symmetric spaces and its application

Cites Work

• A motion of spacelike curves in the Minkowski 3-space and the KdV equation
• A note on the NLS and the Schrödinger flow of maps
• Schrödinger flow of maps into symplectic manifolds
• Geometric realizations of Fordy-Kulish nonlinear Schrödinger systems.
• Schrödinger flows, binormal motion for curves and the second AKNS-hierarchies
• Generalised KdV and MKdV equations associated with symmetric spaces
• Progressive Deformation of a Curved Vortex Filament by its Own Induction
• A soliton on a vortex filament
• Exact envelope-soliton solutions of a nonlinear wave equation

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