Multitime prolongations of single-time ODEs and PDEs

摘要

The main purpose of this paper is to present some methods to create multitime prolongations of single-time evolution ODEs and PDEs. The passing from single-time modeling to multitime evolution is motivated by examples of possible applications in different fields of science. Our original ways to materialize these ideas were: constructing new multitime evolution soliton PDEs as geometrical prolongations of the corresponding single-time PDEs and obtaining some exact multitime soliton solutions; changing some single-time evolution laws described by ODEs into multitime evolution laws (multitime PDEs systems), by accepting that the time is a function of certain parameters; building multitime versions of some significant ODEs and PDEs from electronics, engineering of materials, meteorology etc, in order to obtain a efficient representation of some phenomena including more temporal scales evolving from slow to faster.