Derivative forms of the three-component nonlinear Schrödinger equation and their simplest solutions

Abstract

We propose a sequence of Lax pairs whose compatibility conditions are three-component integrable nonlinear equations. The first equations of this hierarchy are the three-component Kaup–Newell, Chen–Lee–Liu, and Gerdjikov–Ivanov equations. The type of equation depends on an additional parameter \(\alpha\). The proposed form of the three-component Kaup–Newell equation is slightly different from the classical one. We show that the evolution of the components of the simplest nontrivial solutions of these equations is completely determined by the evolution of the length of the solution vector and additional numerical parameters.