We consider the scattering transform for Schrödinger operators with energy dependent
potentials. We prove unique invertibility of the transform when there are no bound states and …

A Crum transformation for the linear problem of the non-focusing nonlinear Schrödinger
(NLS) equation is used to construct the sequence of rational solutions, given in terms of tau …

We consider an inverse scattering problem for Schrödinger operators with energy-
dependent potentials. The inverse problem is formulated as a Riemann-Hilbert problem on a …

We develop a reflectionless inverse scattering theory regarding an energy-dependent
Schrödinger equation. A necessary and sufficient condition for scattering data to recover a …

A family of polynomial τ-functions for the NLS-Toda hierarchy is constructed. The hierarchy
is associated with the homogeneous vertex operator representation of the affine algebra g of …

A nonconservative, reflectionless inverse scattering problem is discussed on an energy
dependent Schrödinger equation. A scattering transform from the potential of the equation to …

The main concepts of the soliton theory and infinite dimensional Hamiltonian Systems,
including AKNS (Ablowitz, Kaup, Newell, Segur) integrable hierarchy of nonlinear evolution …