Group classification of the general evolution equation: local and quasilocal symmetries. (English) Zbl 1128.35010
The authors briefly review their results [P. Bassarab-Horwath, V. Lahno and R. Zhdanov, Acta Appl. Math. 69, 43–94 (2001; Zbl 1054.35002)] on the complete group classification of the general nonlinear evolution equation \(u_t=F(t,x,u,u_x,u_{xx})\), \(\frac{\partial F}{\partial u_{xx}}\neq 0\).
Reviewer: Boris V. Loginov (Ul’yanovsk)
MSC:
| 35A30 | Geometric theory, characteristics, transformations in context of PDEs |
| 58J70 | Invariance and symmetry properties for PDEs on manifolds |
| 35K55 | Nonlinear parabolic equations |
