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arXiv · 1407.0677

Hirota difference equation: IST, Darboux transformation and solitons

Andrei Pogrebkov
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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.

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Andrei Pogrebkov. 2014-07-02. Hirota difference equation: IST, Darboux transformation and solitons. https://doi.org/10.1007/s11232-014-0237-z

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