Euler, N.; Shul’ga, M. W.; Steeb, W.-H. Approximate symmetries and approximate solutions for a multidimensional Landau-Ginzburg equation. (English) Zbl 0764.35096 J. Phys. A, Math. Gen. 25, No. 18, L1095-L1103 (1992). Summary: We give the approximate symmetries for the multidimensional Landau- Ginzburg equation \(\sum_{i=1}^ 3 \partial^ 2 u/\partial x_ i^ 2+\partial u/\partial x_ 4=a_ 1+a_ 2u+\varepsilon u^ n\) where \(n\in{\mathcal R}\) and \(0<\varepsilon\ll 1\). We also construct approximate solutions for this nonlinear equation using the approximate symmetries. Cited in 16 Documents MSC: 35Q55 NLS equations (nonlinear Schrödinger equations) 58J70 Invariance and symmetry properties for PDEs on manifolds 35A30 Geometric theory, characteristics, transformations in context of PDEs Keywords:Lie symmetries PDFBibTeX XMLCite \textit{N. Euler} et al., J. Phys. A, Math. Gen. 25, No. 18, L1095--L1103 (1992; Zbl 0764.35096) Full Text: DOI