On ‘regular’ and ‘anomalous’ solitons of fifth-order equations and an iteration method

A procedure is described for deriving the ‘anomalous’ soliton solutions of the fifth-order Kaup-Kupershmidt (KK) equation; these solutions are compared with the ‘regular’ solitons of the companion Sawada-Kotera (SK) equation. The first few solitons of the KK equation are constructed explicitly and, in a novel departure from Hirotaʹs bilinear transform, an iteration method is presented for obtaining multisoliton solutions of any order.