View source for Idempotent superposition principle

''Maslov superposition principle''

A method used in [[Idempotent analysis|idempotent analysis]] and similar to the well-known superposition principle in quantum theory. Just as the basic equations of quantum mechanics are linear, the Hamilton–Jacobi equation (i.e. the basic equation in classical mechanics; cf. also [[Hamilton–Jacobi theory|Hamilton–Jacobi theory]]) and the [[Bellman equation|Bellman equation]] (i.e. the basic equation for optimization problems) are linear over suitable idempotent semi-rings (cf. [[Idempotent semi-ring|Idempotent semi-ring]]). Using this idea it is possible to generalize classical linear methods to these equations (which are non-linear in the traditional sense); it is useful, e.g., for the explicit construction of their solutions [[#References|[a1]]], [[#References|[a2]]].

====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  V.P. Maslov,   "New superposition principle for optimization problems"  ''Russian Math. Surveys'' , '''42'''  (1987)  (In Russian)</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top">  V.N. Kolokoltsov,   V.P. Maslov,   "Idempotent analysis and applications" , Kluwer Acad. Publ.  (1996)  (In Russian)</TD></TR></table>