The pair-transition-coupled nonlinear Schrödinger equation: The Riemann-Hilbert problem and N-soliton solutions

In this work, the pair-transition-coupled nonlinear Schrödinger (pt-CNLS) equation, which can also be used to describe the propagation of orthogonally polarized optical waves in an isotropic medium, is under investigation. The spectral analysis with 4×4 Lax pairs is performed for the integrable pt-CNLS equations, from which a kind of Riemann-Hilbert problem is strictly formulated. Moreover, N-soliton solutions to the pt-CNLS equation are constructed by using a specific Riemann-Hilbert formulation.