Cross-Newell equations for hexagons and triangles

Details Cross-Newell equations for hexagons and triangles Cross-Newell equations for hexagons and triangles

1999-10-16

arxiv.org/abs/patt-sol/9910004v1

Nonlinear Sciences

Pattern Formation and Solitons

24 pages, 1 figure

Scientific paper

10.1103/PhysRevE.61.2506

The Cross-Newell equations for hexagons and triangles are derived for general real gradient systems, and are found to be in flux-divergence form. Specific examples of complex governing equations that give rise to hexagons and triangles and which have Lyapunov functionals are also considered, and explicit forms of the Cross-Newell equations are found in these cases. The general nongradient case is also discussed; in contrast with the gradient case, the equations are not flux-divergent. In all cases, the phase stability boundaries and modes of instability for general distorted hexagons and triangles can be recovered from the Cross-Newell equations.

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