Fractional Curve Flows and Solitonic Hierarchies in Gravity and Geometric Mechanics

Details Fractional Curve Flows and Solitonic Hierarchies in Gravity and Geometric Mechanics Fractional Curve Flows and Solitonic Hierarchies in Gravity and Geometric Mechanics

2010-07-16

arxiv.org/abs/1007.2866v3

J. Math. Phys. 52: 053514,2011

Physics

Mathematical Physics

latex2e, 11pt, 21 pages; the variant accepted to J. Math. Phys.; new and up--dated references

Scientific paper

10.1063/1.3589964

Methods from the geometry of nonholonomic manifolds and Lagrange-Finsler spaces are applied in fractional calculus with Caputo derivatives and for elaborating models of fractional gravity and fractional Lagrange mechanics. The geometric data for such models are encoded into (fractional) bi-Hamiltonian structures and associated solitonic hierarchies. The constructions yield horizontal/vertical pairs of fractional vector sine-Gordon equations and fractional vector mKdV equations when the hierarchies for corresponding curve fractional flows are described in explicit forms by fractional wave maps and analogs of Schrodinger maps.

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