The essential conditions for soliton solution of the non-local Manakov system.

This paper aims to study and determine the necessary condition of obtaining soliton solutions in multi-component generalizations of the non-local reduction for nonlinear Schrödinger equation with PT-symmetry. We consider particularly square barrier initial conditions. This work includes: evaluating the spectral problem, introducing the Jost solutions and scattering matrix of the Zakharov-Shabat system, and determining discrete eigenvalues. As the main example, we use the Zakharov-Shabat system which corresponds to the Manakov system of nonlinear Schrödinger equation. In addition, three cases of square barrier potential corresponding to symmetric and asymmetric potentials are shown and studied. A multi-soliton configuration is shown to be allowed for multi-component non-local nonlinear Schrödinger equations of the Manakov type. Numerical simulations are used to obtain and illustrate the results that depend on solving a system of equations. [ABSTRACT FROM AUTHOR]