Approximate symmetries and approximate solutions for a multidimensional Landau-Ginzburg equation. (English) Zbl 0764.35096

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.


35Q55 NLS equations (nonlinear Schrödinger equations)
58J70 Invariance and symmetry properties for PDEs on manifolds
35A30 Geometric theory, characteristics, transformations in context of PDEs


Lie symmetries
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