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Dirac-bracket structure in multidimensional mode conversion
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DOI：10.1016/j.cnsns.2011.05.013.png)
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Abstract
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The intersection of two (2n - 1)-dimensional dispersion manifolds D(a) and D(b) in the 2n-dimensional ray phase space P yields a (2n - 2)-dimensional conversion manifold M D(a) boolean AND D(b) that naturally possesses a Dirac-bracket structure that is inherited from the canonical Poisson bracket on ray phase space. The canonical symplectic two-form Omega Omega(parallel to) + Omega(perpendicular to), defined on the 2n-dimensional tangent plane T(z0)P T(z0)M circle plus (T(z0)M)_, can thus be decomposed into the Dirac two-form Omega(parallel to) on the (2n - 2)-dimensional tangent plane T(z0)M at a conversion point z(0) is an element of M. and the symplectic two-form Omega(perpendicular to) on its orthogonal 2-dimensional complement (T(z0)M)(perpendicular to). These two symplectic two-forms are introduced in our analysis of multidimensional mode conversion, where their respective geometrical roles are defined. We note that since the Dirac-bracket structure Omega(parallel to) vanishes identically when n = 1, it represents a new structure in multidimensional (n > 1) mode conversion theory. (C) 2011 Elsevier B.V. All rights reserved.
Keywords:
Dirac-bracket structure
Mode conversion
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