Fourth-Order Pattern Forming PDEs: Partial and Approximate Symmetries.

This paper considers pattern forming nonlinear models arising in the study of thermal convection and continuous media. A primary method for the deriva- tion of symmetries and conservation laws is Noether's theorem. However, in the ab- sence of a Lagrangian for the equations investigated, we propose the use of partial Lagrangians within the framework of calculating conservation laws. Additionally, a nonlinear Kuramoto-Sivashinsky equation is recast into an equation possessing a per- turbation term. To achieve this, the knowledge of approximate transformations on the admissible coefficient parameters is required. A perturbation parameter is suit- ably chosen to allow for the construction of nontrivial approximate symmetries. It is demonstrated that this selection provides approximate solutions. [ABSTRACT FROM AUTHOR]