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This paper constructs perfectly matched layers (PML) for a system of 2DCoupled Nonlinear Schr\"odinger equations with mixed derivatives which arisesin the modeling of gap solitons in nonlinear periodic structures with anon-separable linear part. The PML construction is performed in Laplace Fourierspace via a modal analysis and can be viewed as a complex change of variables.The mixed derivatives cause the presence of waves with opposite phase and groupvelocities, which has previously been shown to cause instability of layerequations in certain types of hyperbolic problems. Nevertheless, here the PMLis stable if the absorption function $\sigma$ lies below a specified threshold.The PML construction and analysis are carried out for the linear part of thesystem. Numerical tests are then performed in both the linear and nonlinearregimes checking convergence of the error with respect to the layer width andshowing that the PML performs well even in many nonlinear simulations.

Perfectly Matched Layers for Coupled Nonlinear Schr\"{o}dinger Equations with Mixed Derivatives