New Types of Derivative Non-linear Schrödinger Equations Related to Kac–Moody Algebra A2(1)

Abstract

We derive a new system of integrable derivative non-linear Schrödinger equations with an L operator, quadratic in the spectral parameter with coefficients belonging to the Kac–Moody algebra A2(1). The construction of the fundamental analytic solutions of L is outlined and they are used to introduce the scattering data, thus formulating the scattering problem for the Lax pair L,M.