On planar compactons with an extended regularity.

Using a Lotka–Volterra type system on a hexagonal lattice we derive and study a novel, strongly nonlinear dispersive equation u t = ∂ x ( u + Δ u ) n , n > 1 , the n -Cubic equation, which supports the formation and propagation of planar compactons endowed with extended regularity at their perimeter. Compactons may be uni-modal or, if n is odd, multi-modal as well. Both evolution and interaction of compactons are presented and discussed. [ABSTRACT FROM AUTHOR]