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 language||English (US)|
|Number of pages||20|
|Journal||IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)|
|State||Published - 1990|
ASJC Scopus subject areas
- Applied Mathematics