Nonlinear bi-integrable couplings of a generalized Kaup–Newell type soliton hierarchy

Abstract

Based on the three-dimensional special linear Lie algebra sl(2,ℝ), a generalized Kaup–Newell type soliton hierarchy is derived, the nonlinear bi-integrable coupling of which is constructed through the semi-direct sum of Lie algebra. The variational identity is used to furnish Hamiltonian structures of the resulting nonlinear evolution equations hierarchies.