Darboux transformation and Nᵗʰ iteration analytical solutions of a new non-local coupled non-linear Schrodinger equations

In this work, a novel integrable system of non-local coupled Schrodinger equations (NCNLSE) is investigated. Specifically, with the help of related Lax representation and zero curvature condition, the NCNLSE are first derived in terms of the parity-time symmetry reduction method. Then based on Darboux transformation, the first, second, and Nth iteration solutions of the NCNLSE are obtained. This paper shows that the results obtained are different from those of the corresponding known local model of coupled non-linear Schrodinger equations.