Inverse problem of variational calculus for nonlinear evolution equations

Details Inverse problem of variational calculus for nonlinear evolution equations Inverse problem of variational calculus for nonlinear evolution equations

2006-03-17

arxiv.org/abs/nlin/0603037v2

Acta Physica Polonica B 1993,38(2007)

Nonlinear Sciences

Exactly Solvable and Integrable Systems

6 pages, no figure,To appear in the June (2007) issue of Acta Physica Polonica B

Scientific paper

We couple a nonlinear evolution equation with an associated one and derive the action principle. This allows us to write the Lagrangian density of the system in terms of the original field variables rather than Casimir potentials. We find that the corresponding Hamiltonian density provides a natural basis to recast the pair of equations in the canonical form. Amongst the case studies presented the KdV and modified KdV pairs exhibit bi-Hamiltonian structure and allow one to realize the associated fields in physical terms

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