On New Hamiltonian Structures of Two Integrable Couplings

Abstract

In this paper, we present new Hamiltonian operators for the integrable couplings of the Ablowitz–Kaup–Newell–Segur hierarchy and the Kaup–Newell hierarchy. The corresponding Hamiltonians allow nontrivial degeneration. Multi-Hamiltonian structures are investigated. The involutive property is proven for the new and known Hamiltonians with respect to the two Poisson brackets defined by the new and known Hamiltonian operators.

Keywords

• integrable coupling
• Hamiltonian structure
• Hamiltonian
• Ablowitz–Kaup–Newell–Segur hierarchy
• Kaup–Newell hierarchy