A bidirectional Kaup-Kupershmidt equation and directionally dependent solitons

Exact multisoliton solutions are obtained for the bidirectional Kaup-Kupershmidt equation that was reported in a recent paper [J. Math. Phys. 42, 2567 (2001)]-this fills the gap that was left in the prior study. These solutions are found to possess the same remarkable, and unusual, property as the solitary-wave solution; namely, their wave profiles are directionally dependent. In particular, solitons are presented which describe multiple "head-on" collisions between single- and double-humped solitary waves. Explicit expressions are given for the first few multisoliton solutions and a procedure is described for constucting the general N-soliton by iteration on the solitons of lower order. (C) 2002 American Institute of Physics.