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Noether's Theorem and the Conservation Laws of the K ORTEWEG ‐ DE V RIES Equation
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.19754870605
Subject(s) - noether's theorem , galilean transformation , conservation law , mathematical physics , burgers' equation , transformation (genetics) , physics , galilean , nonlinear system , lagrangian , classical mechanics , quantum mechanics , biochemistry , chemistry , gene
A method developed recently by the author to derive a continuum of conservation laws by Noether's theorem from the so‐called extended Bäcklund transformations is applied to the K ORTEWEG ‐ DE V RIES equation that describes various nonlinear dispersive wave phenomena in hydrodynamics, plasma physics and solid state physics. Further applications of Noether's theorem concerning this equation are given. It is shown that the Galilean transformation in the present case has an analogous function as Lie's transformation has with respect to the sine‐Gordon equation.