Resonant Geometric Phases for Soliton Equations
The goal of the present paper is to introduce a multidimensional generalization of asymptotic reduction given in a paper by Alber and Marsden , to use this to obtain a new class of solutions that we call resonant solitons, and to study the corresponding geometric phases. The term "resonant solitons" is used because those solutions correspond to a spectrum with multiple points, and they also represent a dividing solution between two different types of solitons. In this sense, these new solutions are degenerate and, as such, will be considered as singular points in the moduli space of solitons.
©1994, American Mathematical Society. Mark Alber thanks The Fields Institute for its kind hospitality during two visits in 1993. We also thank Dave McLaughlin for several helpful suggestions.
Published - AlMa1994a.pdf