Geometric Phases and Monodromy at Singularities

Albers, M. S. and J. E. Marsden

Singular Limits of Dispersive waves, NATO ASI Series C, 320, 273-295

Abstract:

"Phase functions in the quasi-periodic case have important applications in the theory of evolution equations (where they appear in connection with the Whitham equations). We investigate them in the singular (soliton, umbilic soliton and homoclinic) cases. In this paper we consider the umbilic and homoclinic solutions in this context."