The averaging of weakly nonlocal Symplectic Structures

Details The averaging of weakly nonlocal Symplectic Structures The averaging of weakly nonlocal Symplectic Structures

2004-05-10

arxiv.org/abs/nlin/0405018v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

7 pages, Latex

Scientific paper

We consider the averaging of the weakly nonlocal Symplectic Structures corresponding to local evolution PDE's in the Whitham method. The averaging procedure gives the weakly nonlocal Symplectic Structure of Hydrodynamic Type for the corresponding Whitham system. The procedure gives also the "action variables" corresponding to the wave numbers of $m$-phase solutions of initial system which give the additional conservation laws for the Whitham system.

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