Bäcklund Transformations of the Relativistic Schrödinger Equation

Abstract

We study the system of equations obtained on the basis of the relativistic Schrödinger equation and relating the potential, amplitude, and phase functions. Using the methods of the theory of consistency of systems of partial differential equations, we obtain completely integrable systems that relate only two functions of the above three. The systems found are related by Bäcklund transformations.