Rational solutions of a weakly coupled nonlocal nonlinear Schrödinger equation (Q1629340)

Summary: In this article, we investigate an integrable weakly coupled nonlocal nonlinear Schrödinger (WCNNLS) equation including its Lax pair. Afterwards, Darboux transformation (DT) of the weakly coupled nonlocal NLS equation is constructed, and then the degenerated Darboux transformation can be got from Darboux transformation. Applying the degenerated Darboux transformation, the new solutions (\(q^{[1]}\), \(r^{[1]}\)) and self-potential function \((V^{[1]})\) are created from the known solutions (\(q,r\)). The (\(q^{[1]}\), \(r^{[1]}\)) satisfy the parity-time (PT) symmetry condition, and they are rational solutions with two free phase parameters of the weakly coupled nonlocal nonlinear Schrödinger equation. From the plots of solutions, the compression effects of the real refractive index profile and the gain-or-loss distribution are produced.