Noether's Theorem and the Conservation Laws of the KORTEWEG‐DE VRIES Equation
- 1 January 1975
- journal article
- Published by Wiley in Annalen der Physik
- Vol. 487 (6) , 445-455
- https://doi.org/10.1002/andp.19754870605
Abstract
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 KORTEWEG‐DE VRIES 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.Keywords
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