Geodesic
Hirota difference equation: Inverse scattering transform, Darboux transformation, and solitons
Teoretičeskaâ i matematičeskaâ fizika, Tome 181 (2014) no. 3, pp. 538-552

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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.
Keywords: Hirota difference equation, inverse scattering transform
Mots-clés : soliton, Darboux transformation. 
@article{TMF_2014_181_3_a8,
     author = {A. K. Pogrebkov},
     title = {Hirota difference equation: {Inverse} scattering transform, {Darboux} transformation, and solitons},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {538--552},
     publisher = {mathdoc},
     volume = {181},
     number = {3},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2014_181_3_a8/}
}
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A. K. Pogrebkov. Hirota difference equation: Inverse scattering transform, Darboux transformation, and solitons. Teoretičeskaâ i matematičeskaâ fizika, Tome 181 (2014) no. 3, pp. 538-552. http://geodesic.mathdoc.fr/item/TMF_2014_181_3_a8/