Optique géométrique pour des systemes semi-linéaires avec invariance de jauge
The main topic of the book is a study of the properties of solutions of field equations for a scalar field or a spinor field coupled to a Yang-Mills field, and construction of approximate solutions of a special shape. First, in the 60’s, solutions that rapidly oscillated in high frequencies were found by Y. Choquet-Bruhat, using a modification of WKB methods for solutions of linear partial differential equations. Meanwhile, justification for ideas coming from geometric optics was developed for solutions of certain semi-linear or quasi-linear equations. The first part of the book contains an exposition of a structure of the equations. The second part describes families of approximate solutions (to any order), in the shape of single-phase expansions, rapidly oscillating at high frequency. The third part contains a description of exact solutions, asymptotic to previous expansions.