A Bi-Hamiltonian Formulation for Triangular Systems by Perturbations

Details A Bi-Hamiltonian Formulation for Triangular Systems by Perturbations A Bi-Hamiltonian Formulation for Triangular Systems by Perturbations

2001-12-07

arxiv.org/abs/nlin/0112009v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

16 pages, to appear in J. Math. Phys

Scientific paper

10.1063/1.1432775

A bi-Hamiltonian formulation is proposed for triangular systems resulted by perturbations around solutions, from which infinitely many symmetries and conserved functionals of triangular systems can be explicitly constructed, provided that one operator of the Hamiltonian pair is invertible. Through our formulation, four examples of triangular systems are exhibited, which also show that bi-Hamiltonian systems in both lower dimensions and higher dimensions are many and varied. Two of four examples give local 2+1 dimensional bi-Hamiltonian systems and illustrate that multi-scale perturbations can lead to higher-dimensional bi-Hamiltonian systems.

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