Canonical structure of the coupled Korteweg–de Vries equations

Abstract

The inverse problem of variational calculus is solved for the coupled Korteweg–de Vries equations resulting from a complex Lax pair. The system is found to be characterized by a second-order degenerate Lagrangian density having some common feature with the well-known Morse–Feshbach Lagrangian. The Hamiltonian structure is examined using Dirac's theory of constraints. PACS Nos.: 47.20.Ky, 42.81.Dp