TY - JOUR
T1 - Computation, dimensionality, and zero-dissipation limit of the ginzburg-landau wave equation
AU - Yang, Yisong
N1 - Copyright:
Copyright 2010 Elsevier B.V., All rights reserved.
PY - 1990
Y1 - 1990
N2 - 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.
AB - 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.
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U2 - 10.1093/imamat/45.2.175
DO - 10.1093/imamat/45.2.175
M3 - Article
AN - SCOPUS:0025567701
SN - 0272-4960
VL - 45
SP - 175
EP - 194
JO - IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)
JF - IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)
IS - 2
ER -