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Zbl 0764.35096
Euler, N.; Shul'ga, M.W.; Steeb, W.-H.
Approximate symmetries and approximate solutions for a multidimensional Landau-Ginzburg equation. (English)
[J] J. Phys. A, Math. Gen. 25, No.18, L1095-L1103 (1992). ISSN 0305-4470

Summary: We give the approximate symmetries for the multidimensional Landau- Ginzburg equation $\sum\sb{i=1}\sp 3 \partial\sp 2 u/\partial x\sb i\sp 2+\partial u/\partial x\sb 4=a\sb 1+a\sb 2u+\varepsilon u\sp n$ where $n\in{\cal R}$ and $0<\varepsilon\ll 1$. We also construct approximate solutions for this nonlinear equation using the approximate symmetries.

MSC 2000:: *35Q55 NLS-like (nonlinear Schroedinger) equations
58J70 Invariance and symmetry properties
35A30 Geometric theory for PDE, transformations

Keywords: Lie symmetries

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Zentralblatt MATH Berlin [Germany]