On quintic equations with a linear window

We study a quintic dispersive equation ut=[au2+b(uuxx+βux2)+c(uu4x+2q1uxu3x+q2uxx2)]x and show that if β=q1=−q2β=q1=−q2, it may be cast into vt=[vLωu]xvt=[vLωu]x, where v=uωv=uω, ω=2β+1ω=2β+1 and LωLω is a fourth order linear operator. This enables to construct traveling patterns via superposition of solutions. A plethora of bell-shaped, multi-humped and asymmetric compacton, is found. Their interaction ranges from being almost elastic to a noisy one, including fusion of bell-shaped compactons and anti-compactons into robust asymmetric structures. A stationary, zero-mass, doublet-like compacton is found to be an attractor of topologically similar, zero-mass, excitations.