Fractional Curve Flows and Solitonic Hierarchies in Gravity and Geometric Mechanics

Abstract

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.

arXiv commentlatex2e, 11pt, 21 pages; the variant accepted to J. Math. Phys.; new and up--dated references

References in corpus (4)

• Lagrangian formulation of classical fields within Riemann-Liouville fractional derivatives
• Einstein Gravity as a Nonholonomic Almost Kahler Geometry, Lagrange-Finsler Variables, and Deformation Quantization
• Curve Flows in Lagrange-Finsler Geometry, Bi-Hamiltonian Structures and Solitons
• Fedosov Quantization of Fractional Lagrange Spaces

Cited by in corpus (6)

• Fractional Dynamics from Einstein Gravity, General Solutions, and Black Holes
• Fractional Nonholonomic Ricci Flows
• Extending the D'Alembert Solution to Space-Time Modified Riemann-Liouville Fractional Wave Equations
• Geometrical enhancement of the electric field: Application of fractional calculus in nanoplasmonics
• Quantum geometric information flows and relativistic generalizations of G. Perelman thermodynamics for nonholonomic Einstein systems with black holes and stationary solitonic hierarchies
• Fractional Analogous Models in Mechanics and Gravity Theories