Reciprocal transformations of Hamiltonian operators of hydrodynamic type: nonlocal Hamiltonian formalism for linearly degenerate systems

Details Reciprocal transformations of Hamiltonian operators of hydrodynamic type: nonlocal Hamiltonian formalism for linearly degenerate systems Reciprocal transformations of Hamiltonian operators of hydrodynamic type: nonlocal Hamiltonian formalism for linearly degenerate systems

2002-12-10

arxiv.org/abs/nlin/0212026v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

26 pages

Scientific paper

10.1063/1.1542921

Reciprocal transformations of Hamiltonian operators of hydrodynamic type are investigated. The transformed operators are generally nonlocal, possessing a number of remarkable algebraic and differential-geometric properties. We apply our results to linearly degenerate semi-Hamiltonian systems in Riemann invariants. Since all such systems are linearizable by appropriate (generalized) reciprocal transformations, our formulae provide an infinity of mutually compatible nonlocal Hamiltonian structures, explicitly parametrized by arbitrary functions of one variable.

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