We demonstrate the possibility to reproduce the experimental evolution of an interface,
here a flame front, through the trajectory of a few poles whose position in the complex
plane expresses the interface shape. These poles are analytical solutions of the Sivashinsky
equation and they evolve according to an ordinary differential equation. The direct
comparison with experimental flame fronts propagating in a quasi-two-dimensional configuration
is made at the nonlinear but deterministic stages of the front dynamics, reproducing
a cell creation and fusion process. At later times, when the front is sensitive to
noise as in the Kardar-Parisi-Zhang equation, we demonstrate that the cell size distribution
is still ruled by the pole attractive nature.
