Systems of conservation laws within the framework of the projective theory of congruences: the Lévy transformations of semiHamiltonian systems
Abstract
We continue the investigation of the recently proposed geometric correspondence between systems of conservation laws and congruences of lines in projective space. The relationship between the `additional' conservation laws and hypersurfaces conjugate to a congruence is established, thus providing a basis for the Lévy transformations of semiHamiltonian systems. Similarly, the correspondence between commuting flows and certain families of planes (containing the lines of the congruence) gives rise to the adjoint Lévy transformations.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 October 2000
 DOI:
 10.1088/03054470/33/39/309
 Bibcode:
 2000JPhA...33.6935F