Lanczos-Chebyshev pseudospectral methods for wave-propagation problems

Peter Y.P. Chen, Boris A. Malomed

Research output: Contribution to journalArticlepeer-review

Abstract

The pseudospectral approach is a well-established method for studies of the wave propagation in various settings. In this paper, we report that the implementation of the pseudospectral approach can be simplified if power-series expansions are used. There is also an added advantage of an improved computational efficiency. We demonstrate how this approach can be implemented for two-dimensional (2D) models that may include material inhomogeneities. Physically relevant examples, taken from optics, are presented to show that, using collocations at Chebyshev points, the power-series approximation may give very accurate 2D soliton solutions of the nonlinear Schrödinger (NLS) equation. To find highly accurate numerical periodic solutions in models including periodic modulations of material parameters, a real-time evolution method (RTEM) is used. A variant of RTEM is applied to a system involving the copropagation of two pulses with different carrier frequencies, that cannot be easily solved by other existing methods.

Original languageEnglish
Pages (from-to)1056-1068
Number of pages13
JournalMathematics and Computers in Simulation
Volume82
Issue number6
DOIs
StatePublished - Feb 2012

Keywords

  • Nonlinear Schrödinger equations
  • Pseudospectral Chebyshev method
  • Real-time evolution method
  • Solitary wave propagation
  • Waves in complex media

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