Hirota difference equation: IST, Darboux transformation and solitons
arXiv:1407.0677 · doi:10.1007/s11232-014-0237-z
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.
arXiv comment17 pages
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