New hierarchy of integrable system bi-Hamiltonian structure and constrained flows (Q1579829)

The paper deals with the hierarchy of integrable systems associated with the unstable nonlinear Schrödinger equation. To derive the bi-Hamiltonian structure of the system the authors use the spectral gradient approach and a trace identity. As a consequence they obtain a new Lax operator of the constrained flows which is the generalization of the classical \(r\)-matrix and one can adopt the separation of the variable method to solve them explicitly.