Abstract
We consider the direct and inverse problems for the Hirota difference equation. We introduce the Jost solutions and scattering data and describe their properties. In a special case, we show that the Darboux transformation allows finding the evolution in discrete time and obtaining a recursive procedure for sequentially constructing the Jost solution at an arbitrary time for a given initial value. We consider some properties of the soliton solutions.
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Dedicated to the 75th birthday of Andrei Alekseevich Slavnov
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Pogrebkov, A.K. Hirota difference equation: Inverse scattering transform, darboux transformation, and solitons. Theor Math Phys 181, 1585–1598 (2014). https://doi.org/10.1007/s11232-014-0237-z
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DOI: https://doi.org/10.1007/s11232-014-0237-z