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 
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/
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     author = {N. N. Romanova},
     title = {$N${-Soliton} solution {\textquotedblleft}on a pedestal{\textquotedblright} of the modified {Korteweg{\textendash}de~Vries} equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {205--214},
     year = {1979},
     volume = {39},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1979_39_2_a6/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] T. L. Perelman, A. Kh. Fridman, M. M. Elyashevich, ZhETF, 66 (1974), 1316 | MR

[2] T. Maxworthy, L. G. Redekopp, Icarus, 29 (1976), 261 | DOI

[3] C. S. Gardner, J. M. Greene, M. D. Kruskal, R. M. Miura, Phys. Rev. Lett., 19 (1967), 1095 | DOI

[4] M. Wadati, J. Phys. Soc. Japan, 34 (1973), 1289 | DOI | MR | Zbl

[5] V. E. Zakharov, A. B. Shabat, ZhETF, 64 (1973), 1639