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A high-order numerical method for the nonlinear Helmholtz equation in multidimensional layered media |
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| Authors: | G Baruch G Fibich S Tsynkov |
| Institution: | 1. Department of Applied Mathematics, School of Mathematical Sciences, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel;2. Department of Mathematics, North Carolina State University, Box 8205, Raleigh, NC 27695, USA |
| Abstract: | We present a novel computational methodology for solving the scalar nonlinear Helmholtz equation (NLH) that governs the propagation of laser light in Kerr dielectrics. |
| Keywords: | Nonlinear optics Kerr nonlinearity Inhomogeneous medium Material discontinuities Discontinuous coefficients Layered medium Nonparaxiality Forward scattering Backscattering (Narrow) solitons Paraxial approximation Nonlinear Schrö dinger equation Arrest of collapse Finite-difference approximation Compact scheme High-order method Artificial boundary conditions (ABCs) Two-way ABCs Traveling waves Complex valued solutions Freché t differentiability Newton&rsquo s method |
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