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Numerically modelling semidirect product geodesics
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DOI：10.1088/1751-8121/ae1338.png)
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En 中文
This paper numerically investigates Euler-Poincar & eacute; equations arising from a self-semidirect product group structure. A monolithic energy-preserving continuous Galerkin finite element method is used to study geodesic equations associated with the semidirect product of the diffeomorphism group on a circle with itself. Theoretically predicted peakon solutions are observed as an emergent behaviour. In addition, complicated nonlinear transfers of energy are associated with the semidirect product coupling, where amongst various nonlinear interactions, we observe coupled peakon behaviour. We show that the observed peakon-locking behaviour is expected analytically as an admissible singular solution of the dynamical system. A mimetic (C-grid) finite difference method is used to study the geodesic flow of the semidirect product of the volume preserving diffeomorphism group with itself, where similar coupling behaviour is observed in the vorticity variables. We also investigate coadjoint and Lie-Poisson structures in the context of geodesic equations on semidirect product groups, where the underlying group is first extended by central extension or semidirect product.
Keyword:
semidirect product of groups
diffeomorphism
geodesic
extension
期刊
J
IF:
2.1
论文数:
264
被引数:
0
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GEODESIC FLOW ON EXTENDED BOTT–VIRASORO GROUP AND GENERALIZED TWO-COMPONENT PEAKON TYPE DUAL SYSTEMS
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