A Ya Maltsev 2005 J. Phys. A: Math. Gen. 38 637 doi:10.1088/0305-4470/38/3/007
A Ya Maltsev
Show affiliationsWe consider the special type of field-theoretical 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 m-phase solutions of the initial system which give the additional conservation laws for the Whitham system.
Issue 3 (21 January 2005)
Received 30 June 2004, in final form 16 November 2004
Published 23 December 2004
A Ya Maltsev 2005 J. Phys. A: Math. Gen. 38 637
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