Geodesic
Integrating the Korteweg--de Vries Equation with a Self-Consistent Source and ``Steplike'' Initial Data
Teoretičeskaâ i matematičeskaâ fizika, Tome 129 (2001) no. 1, pp. 38-54

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It is shown that “steplike” solutions of the Korteweg–de Vries equation with a self-consistent source can be found by the inverse scattering method for the Sturm–Liouville operator on the entire real line. 
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     author = {G. U. Urazboev and A. B. Khasanov},
     title = {Integrating the {Korteweg--de} {Vries} {Equation} with a {Self-Consistent} {Source} and {``Steplike''} {Initial} {Data}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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G. U. Urazboev; A. B. Khasanov. Integrating the Korteweg--de Vries Equation with a Self-Consistent Source and ``Steplike'' Initial Data. Teoretičeskaâ i matematičeskaâ fizika, Tome 129 (2001) no. 1, pp. 38-54. http://geodesic.mathdoc.fr/item/TMF_2001_129_1_a4/