On soliton solutions of the KaupKupershmidt equation. I. Direct bilinearisation and solitary wave
Abstract
In this first of two papers (designated I and II [Physica D 137 (2000) 34]), a direct procedure is given for bilinearising the KaupKupershmidt and SawadaKotera equations. It is found that, whereas the SawadaKotera equation can be written in bilinear form in two distinct ways (which are shown to be equivalent), the KaupKupershmidt equation has a single bilinear representation. This distinguishing feature, which has previously received no explanation, has consequences for obtaining the soliton solutions of these two closely related fifthorder integrable equations. The ‘anomalous’ solitary wave of the KaupKupershmidt equation is reconstructed, and a simplified approach to obtaining its Nsoliton solutions is proposed. This provides the basis for constructing these solutions explicitly in II.
 Publication:

Physica D Nonlinear Phenomena
 Pub Date:
 March 2000
 DOI:
 10.1016/S01672789(99)001669
 Bibcode:
 2000PhyD..137...25P