The tri-Hamiltonian dual system of supersymmetric two boson system

• The dual system of the supersymmetric two boson system is constructed through the approach of tri-Hamiltonian duality.
• The bi-Hamiltonian structure and a new linear spectral problem for the dual sTB system are presented.
• The connection of the dual sTB system with the N=2N=2 supersymmetric Camassa–Holm equation have been established.
• A new linear spectral problem for the N=2N=2 supersymmetric Camassa–Holm equation is presented.

The dual system of the supersymmetric two boson system is constructed through the approach of tri-Hamiltonian duality, and inferred from this duality, its zero-curvature representation is also figured out. Furthermore, the dual system is shown to be equivalent to a N=2N=2 supersymmetric Camassa–Holm equation, and this relation results in a new linear spectral problem for the N=2N=2 supersymmetric Camassa–Holm equation.