Analytical properties of solutions to a system of nonlinear partial differential equations

Symmetries of a class of nonlinear third-order partial differential equations

“…These waves interact producing a ripple of low amplitude compactonanticompacton pairs. The Fuchssteiner-Fokas-Camassa-Holm (FFCH) equation 4) first arose in the work of Fuchssteiner and Fokas [25,27] using a bi-Hamiltonian approach; we remark that it is only implicitly written in [27] -see equations (26e) and (30) in this paper -though is explicitly written down in [25]. It has recently been rederived by Camassa and Holm [9] from physical considerations as a model for dispersive shallow water waves.…”

“…Three special cases of (1.1) have appeared recently in the literature. Up to some rescalings, these are: (i), the Fornberg-Whitham equation [28,58,59], for the parameters ǫ = 1, α = −1, β = 3 and κ = 1 2 , (ii), the Rosenau-Hyman equation [54] for the parameters ǫ = 0, α = 1, β = 3 and κ = 0, and (iii), the Fuchssteiner-Fokas-Camassa-Holm equation [9,10,25,27] for the parameters ǫ = 1, α = −1 and β = 2.…”