Integrable G-strands on semisimple Lie groups

François Gay-Balmaz; Darryl D. Holm; Tudor S. Ratiu

doi:10.1088/1751-8113/47/7/075201

Integrable G-strands on semisimple Lie groups

François Gay-Balmaz
, Darryl D. Holm
, Tudor S. Ratiu

Research output: Contribution to journal › Article › peer-review

Abstract

The present paper derives systems of partial differential equations that admit a quadratic zero curvature representation for an arbitrary real semisimple Lie algebra. It also determines the general form of Hamiltons principles and Hamiltonians for these systems, and analyzes the linear stability of their equilibrium solutions in the examples of so(3) and sl(2,R).

Original language	English
Article number	075201
Journal	Journal of Physics A: Mathematical and Theoretical
Volume	47
Issue number	7
DOIs	https://doi.org/10.1088/1751-8113/47/7/075201
Publication status	Published - 21 Feb 2014

Keywords

EulerPoincaré equation
Hamilton principle
integrable Hamiltonian systems
semisimple Lie groups
symmetry reduction
zero curvature representation

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10.1088/1751-8113/47/7/075201

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title = "Integrable G-strands on semisimple Lie groups",

abstract = "The present paper derives systems of partial differential equations that admit a quadratic zero curvature representation for an arbitrary real semisimple Lie algebra. It also determines the general form of Hamiltons principles and Hamiltonians for these systems, and analyzes the linear stability of their equilibrium solutions in the examples of so(3) and sl(2,R).",

keywords = "EulerPoincar{\'e} equation, Hamilton principle, integrable Hamiltonian systems, semisimple Lie groups, symmetry reduction, zero curvature representation",

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AU - Ratiu, Tudor S.

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AB - The present paper derives systems of partial differential equations that admit a quadratic zero curvature representation for an arbitrary real semisimple Lie algebra. It also determines the general form of Hamiltons principles and Hamiltonians for these systems, and analyzes the linear stability of their equilibrium solutions in the examples of so(3) and sl(2,R).

KW - EulerPoincaré equation

KW - Hamilton principle

KW - integrable Hamiltonian systems

KW - semisimple Lie groups

KW - symmetry reduction

KW - zero curvature representation

UR - https://www.scopus.com/pages/publications/84893606823

U2 - 10.1088/1751-8113/47/7/075201

DO - 10.1088/1751-8113/47/7/075201

M3 - Article

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JO - Journal of Physics A: Mathematical and Theoretical

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ER -

Integrable G-strands on semisimple Lie groups

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Keywords

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