A perfectly matched layer for the absorption of electromagnetic waves
Journal of Computational Physics
Perfectly matched absorbing layers for the paraxial equations
Journal of Computational Physics
On the analysis and construction of perfectly matched layers for the linearized Euler equations
Journal of Computational Physics
Absorbing PML boundary layers for wave-like equations
Applied Numerical Mathematics - Special issue on absorbing boundary conditions
Additive Runge-Kutta schemes for convection-diffusion-reaction equations
Applied Numerical Mathematics
Stability of perfectly matched layers, group velocities and anisotropic waves
Journal of Computational Physics
Absorbing Boundary Conditions for One-dimensional Nonlinear Schrödinger Equations
Numerische Mathematik
A new absorbing layer for elastic waves
Journal of Computational Physics
Perfectly matched layers in photonics computations: 1D and 2D nonlinear coupled mode equations
Journal of Computational Physics
A perfectly matched layer approach to the nonlinear Schrödinger wave equations
Journal of Computational Physics
Numerical solution to coupled nonlinear Schrödinger equations on unbounded domains
Mathematics and Computers in Simulation
Journal of Computational and Applied Mathematics
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This paper constructs perfectly matched layers (PML) for a system of 2D coupled nonlinear Schrodinger equations with mixed derivatives which arises in the modeling of gap solitons in nonlinear periodic structures with a non-separable linear part. The PML construction is performed in Laplace-Fourier space 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 group velocities, which has previously been shown to cause instability of layer equations in certain types of hyperbolic problems. Nevertheless, here the PML is stable if the absorption function @s lies below a specified threshold. The PML construction and analysis are carried out for the linear part of the system. Numerical tests are then performed in both the linear and nonlinear regimes checking convergence of the error with respect to the layer width and showing that the PML performs well even in many nonlinear simulations.