Basic Concepts

Solitons are mathematical objects which arise as solutions of certain non-linear wave equations. This class is a rapidly growing one and the reasons for current interest are threefold. First, methods have been found for finding these solutions analytically and therefore exactly, and ideas on their “completeness” have emerged. Second solitons have mathematical properties which make them particle-like and in those contexts of non-linear physics where they arise they are the natural elementary excitations. Third those contexts of non-linear physics are proving to embrace the whole of modern physics itself.