Methods of symplectic and complex geometry have recently given important information about the phase-space geometry of nonlinear equations (see, for example, Ercolani, Forest, McLaughlin, and Montgomery [1987], Ercolani [1989], Ercolani and McLaughlin [1991]' McLaughlin and Overman [1993]). A few specific examples are as follows. From the point of view of complex geometry, the reality condition...

The main contribution of this work consists of developing a new surface smoothing method. The method preserves sharp variation points of the surface normals and is good for stable extraction of perceptually salient ridges and ravines. The method is based on a discrete nonlinear diffusion process (iterative nonlinear averaging) applied to the surface normals. We demonstrate applicability of the ...

Nonlinear resonant magnetohydrodynamic (MHD) waves are studied in weakly dissipative isotropic plasmas in cylindrical geometry. This geometry is suitable and is needed when one intends to study resonant MHD waves in magnetic flux tubes (e.g. for sunspots, coronal loops, solar plumes, solar wind, the magnetosphere, etc.) The resonant behaviour of slow MHD waves is confined in a narrow dissipativ...