Hirota difference equation: IST, Darboux transformation and solitons

Abstract

Direct and inverse problems for the Hirota difference equation are considered. Jost solutions and scattering data are introduced and their properties are presented. Darboux transformation in a special case is shown to give evolution with respect to discrete time and a recursion procedure for consequent construction of the Jost solution at arbitrary time, if the initial value is given. Some properties of the soliton solutions are discussed.

17 pages

References in corpus (2)

• Backlund transformations for difference Hirota equation and supersymmetric Bethe ansatz
• Commutator identities on associative algebras and integrability of nonlinear pde's