Weakly nonlocal symplectic structures, Whitham method and weakly nonlocal symplectic structures of hydrodynamic type
Abstract
We consider the special type of fieldtheoretical symplectic structures called weakly nonlocal. The structures of this type are, in particular, very common for integrable systems such as KdV or NLS. We introduce here the special class of weakly nonlocal symplectic structures which we call weakly nonlocal symplectic structures of hydrodynamic type. We investigate then the connection of such structures with the Whitham averaging method and propose the procedure of 'averaging' the weakly nonlocal symplectic structures. The averaging procedure gives the weakly nonlocal symplectic structure of hydrodynamic type for the corresponding Whitham system. The procedure also gives 'action variables' corresponding to the wave numbers of mphase solutions of the initial system which give the additional conservation laws for the Whitham system.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 January 2005
 DOI:
 10.1088/03054470/38/3/007
 arXiv:
 arXiv:nlin/0405060
 Bibcode:
 2005JPhA...38..637M
 Keywords:

 Nonlinear Sciences  Exactly Solvable and Integrable Systems
 EPrint:
 64 pages, Latex