Classification of phase singularities for complex scalar waves and their bifurcations

摘要: Motivated by the importance and universal character of phase singularities which were clarified recently, we study local structure equi-phase loci near dislocation locus complex valued planar spatial waves, from viewpoint singularity theory differentiable mappings, initiated Whitney Thom. The classification is reduced to curves radial transformations due du Plessis, Gaffney Wilson. Then fold are classified into hyperbolic elliptic singularities. We show that never realized any Helmholtz while in fact. Moreover, realizability Whitney's cusp, as well its bifurcation problem, considered order explain three point In this paper, treat linear waves mainly, developing basic method, method jets transversality, applicable also nonlinear waves.