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 ut=∂x(u+Δu)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.