Lump Solutions to the BKP Equation

Abstract

The BKP equation (Date, Jimbo, Kashiwara and Miwa 1981, Jimbo and Miwa 1983)

$${({{\rm{u}}_{\rm{t}}} + 15{\rm{u}}{{\rm{u}}_{{\rm{3x}}}} + 15{\rm{u}}_{\rm{x}}^{\rm{3}} - 15{{\rm{u}}_{\rm{x}}}{{\rm{u}}_{\rm{y}}} + {{\rm{u}}_{{\rm{5x}}}})_{\rm{x}}} - 5{{\rm{u}}_{{\rm{3x,y}}}} - 5{{\rm{u}}_{{\rm{yy}}}} - 0,$$

(1) is a 2+1 dimensional generalisation of the Caudrey-Dodd-Gibbon-Sawada-Kotera equation (Caudrey, Dodd and Gibbon 1976, Sawada and Kotera 1974). This equation arises from the B-type Lie algebras as opposed to the KP equation which arises from the A-type algebras.