Preliminary group classification of a class of fourth-order evolution equations. (English) Zbl 1202.35011
Summary: We perform preliminary group classification of a class of fourth-order evolution equations in one spatial variable. Following the approach developed by P. Basarab-Horwath et al. [Acta Appl. Math. 69, No. 1, 43–94 (2001; Zbl 1054.35002)], we construct all inequivalent partial differential equations belonging to the class in question which admit semisimple Lie groups. In addition, we describe all fourth-order evolution equations from the class under consideration which are invariant under solvable Lie groups of dimension \(n\leq 4\). We have constructed all Galilei-invariant equations belonging to the class of evolution differential equations under study. The list of so obtained invariant equations contains both the well-known fourth-order evolution equations and a variety of new ones possessing rich symmetry and as such may be used to model nonlinear processes in physics, chemistry, and biology.
Editorial remark: No review copy delivered
Editorial remark: No review copy delivered
MSC:
| 35A30 | Geometric theory, characteristics, transformations in context of PDEs |
| 35K55 | Nonlinear parabolic equations |
| 58J70 | Invariance and symmetry properties for PDEs on manifolds |
Citations:
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