On the direct construction of the inverse scattering operators of integrable nonlinear Hamiltonian systems

Abstract

We show that the mere knowledge of a single symmetry propagator would suffice to construct the Lax operators for the inverse scattering scheme associated with an integrable physical system with one spatial dimension. This construction supplements in an important way the integrability test scheme of Chen, Lee and Liu. A discussion about the feasibility of the above scheme to the integrable systems with higher spatial dimensions is also presented.