Geodesic
$N$-Soliton solution ``on a pedestal'' of the modified Korteweg--de~Vries equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 39 (1979) no. 2, pp. 205-214

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The inverse scattering technique is used to obtain an $N$-soliton solution (which tends to a constant as $x\to\pm\infty$), of the modified Korteweg–de Vries equation with negative sign of the nonlinear term. 
@article{TMF_1979_39_2_a6,
     author = {N. N. Romanova},
     title = {$N${-Soliton} solution ``on a pedestal'' of the modified {Korteweg--de~Vries} equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {205--214},
     publisher = {mathdoc},
     volume = {39},
     number = {2},
     year = {1979},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1979_39_2_a6/}
}
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N. N. Romanova. $N$-Soliton solution ``on a pedestal'' of the modified Korteweg--de~Vries equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 39 (1979) no. 2, pp. 205-214. http://geodesic.mathdoc.fr/item/TMF_1979_39_2_a6/