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Non-standard construction of Hamiltonian structures. (English) Zbl 0939.70020
A method recently developed by the second author [J. Phys. A, Math. Gen. 29, No. 3, 667-674 (1996; Zbl 0924.58022)] for the construction of Hamiltonian structures in field theory without the use of a Lagrangian is presented. The application of the method demands the knowledge of a constant of motion and a solution of the symmetry equation. The method is applied to the heat equation, the time-depended Schrödinger equation, the KdV, the Burgers and Harry-Dym equations.

MSC:
70S05 Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems
70H05 Hamilton’s equations
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