Curve Flows and Solitonic Hierarchies Generated by (Semi) Riemannian Metrics

Details Curve Flows and Solitonic Hierarchies Generated by (Semi) Riemannian Metrics Curve Flows and Solitonic Hierarchies Generated by (Semi) Riemannian Metrics

2006-08-09

arxiv.org/abs/math-ph/0608024v1

Physics

Mathematical Physics

39 pages, latex2e

Scientific paper

We investigate bi-Hamiltonian structures and related mKdV hierarchy of solitonic equations generated by (semi) Riemannian metrics and curve flow of non-stretching curves. The corresponding nonholonomic tangent space geometry is defined by canonically induced nonlinear connections, Sasaki type metrics and linear connections. One yields couples of generalized sine-Gordon equations when the corresponding geometric curve flows result in hierarchies on the tangent bundle described in explicit form by nonholonomic wave map equations and mKdV analogs of the Schrodinger map equation.

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