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- W2952484404 abstract "Motivated by the importance and universal character of phase singularitieswhich are clarified recently, we study the local structure of equi-phaseloci near the dislocation locus of complex valued planar and spatial waves,from the viewpoint of singularity theory of differentiable mappings, initiatedby H. Whitney and R. Thom. The classification of phase-singularitiesare reduced to the classification of planar curves by radial transformationsdue to the theory of A. du Plessis, T. Gaffney and L. Wilson. Then foldsingularities are classified into hyperbolic and elliptic singularities. Weshow that the elliptic singularities are never realized by any Helmholtzwaves, while the hyperbolic singularities are realized in fact. Moreover,the classification and realizability of Whitney’s cusp, as well as its bifurcationproblem are considered in order to explain the three points bifurcationof phase singularities. In this paper, we treat the dislocation of linearwaves mainly, developing the basic and universal method, the method ofjets and transversality, which is applicable also to non-linear waves." @default.
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- W2952484404 date "2006-01-01" @default.
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- W2952484404 title "Classification of phase singularities for complex scalar waves" @default.
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