Summary: Two local conservation laws of the equation are used to define two Lagrange-type transformations into mass and momentum space. These mappings help to identify new integrable cases , , , transform conventional solitary waves into compactons – solitary waves on a compactum – and relate certain soliton-carrying systems with compacton-carrying systems. Integrable equations are transformed into new integrable equations, and interaction of -solitons of the -KdV is thus projected into an interaction in a compact domain from which ordered stationary compactons emerge. The interaction of traveling compactons is the image of super-imposed equilibria of the corresponding soliton equation. For , the potential form of the equation may also be cast into a conserved form and thus transformed, yielding generalized Dym and Wadati equations and two new integrable cases. It is shown that is integrable and supports compact kinks.
|35Q53||KdV-like (Korteweg-de Vries) equations|