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N OETHER'S Theorem and Higher Conservation Laws in Ultrashort Pulse Propagation
Author(s) -
Steudel H.
Publication year - 1975
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.19754870306
Subject(s) - noether's theorem , conservation law , infinitesimal , transformation (genetics) , pulse (music) , mathematical physics , physics , law , mathematics , mathematical analysis , quantum mechanics , biochemistry , chemistry , lagrangian , voltage , gene , political science
L AMB has constructed a number of local conservation laws for the differential equation σ τ = sin σ describing ultrashort pulse propagation in a resonant medium. On the other hand it is known that from any solution of this equation others may be found by B ÄCKLUND transformation. In this paper we introduce extended B ÄCKLUND transformations B a and compose them to form infinitesimal invariance transformations B a+ε B a −1from which via N OETHER'S theorem a system of conservation laws follows. Some of them are recognized as L AMB'S conservation laws. Another conservation law results from a scale invariance called L IE'S transformation.