A Bi-Hamiltonian Formulation for Triangular Systems by Perturbations
arXiv:nlin/0112009 · doi:10.1063/1.1432775
Abstract
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.
16 pages, to appear in J. Math. Phys
References in corpus (6)
- Integrable Theory of the Perturbation Equations
- The Bi-Hamiltonian Structure of the Perturbation Equations of KdV Hierarchy
- Integrable Coupled KdV Systems
- Extending Hamiltonian Operators to Get Bi-Hamiltonian Coupled KdV Systems
- On integrability of a (2+1)-dimensional perturbed Kdv equation
- A Class of Coupled KdV systems and Their Bi-Hamiltonian Formulations