期刊
NONLINEARITY
卷 27, 期 6, 页码 1445-1469出版社
IOP Publishing Ltd
DOI: 10.1088/0951-7715/27/6/1445
关键词
zero curvature representation; Lax pair; Euler-Poincare equations; geometric mechanics; integrable systems
资金
- FCCA from the European Research Council [267382]
- European Research Council (ERC) [267382] Funding Source: European Research Council (ERC)
We discuss three examples in which one may extend integrable Euler-Poincare ordinary differential equations to integrable Euler-Poincare partial differential equations in the matrix G-Strand context. After describing matrix G-Strand examples for SO(3) and SO(4) we turn our attention to SE(3) where the matrix G-Strand equations recover the exact rod theory in the convective representation. We then find a zero curvature representation of these equations and establish the conditions under which they are completely integrable. Thus, the G-Strand equations turn out to be a rich source of integrable systems. The treatment is meant to be expository and most concepts are explained in examples in the language of vectors in R-3.
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