Geodesic
Positons: Slowly Decreasing Analogues of Solitons
Teoretičeskaâ i matematičeskaâ fizika, Tome 131 (2002) no. 1, pp. 44-61

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We present an introduction to positon theory, almost never covered in the Russian scientific literature. Positons are long-range analogues of solitons and are slowly decreasing, oscillating solutions of nonlinear integrable equations of the KdV type. Positon and soliton-positon solutions of the KdV equation, first constructed and analyzed about a decade ago, were then constructed for several other models: for the mKdV equation, the Toda chain, the NS equation, as well as the sinh-Gordon equation and its lattice analogue. Under a proper choice of the scattering data, the one-positon and multipositon potentials have a remarkable property: the corresponding reflection coefficient is zero, but the transmission coefficient is unity (as is known, the latter does not hold for the standard short-range reflectionless potentials). 
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V. B. Matveev. Positons: Slowly Decreasing Analogues of Solitons. Teoretičeskaâ i matematičeskaâ fizika, Tome 131 (2002) no. 1, pp. 44-61. http://geodesic.mathdoc.fr/item/TMF_2002_131_1_a4/