Computation, dimensionality, and zero-dissipation limit of the ginzburg-landau wave equation

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Abstract

In this paper, convergence is proved and optimal error estimates are obtained for the Galerkin approximation scheme for computing spatially period solutions of the Ginzburg-Landau wave equation. Using this convergent scheme, we carry out a series of numerical experiments towards an understanding of the finite dimensionality of the wave motion evolving from a small neighbourhd of the zero solution. In the zerodissipation Limit, we show that the solutions approach those of the cubic SchrÖdinger equation.

Original languageEnglish (US)
Pages (from-to)175-194
Number of pages20
JournalIMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)
Volume45
Issue number2
DOIs
StatePublished - 1990

ASJC Scopus subject areas

  • Applied Mathematics

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