Geodesic
Integrable initial boundary value problems
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 9 (2002) no. 2, pp. 261-267 
I. T. Habibullin. Integrable initial boundary value problems. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 9 (2002) no. 2, pp. 261-267. http://geodesic.mathdoc.fr/item/JMAG_2002_9_2_a12/
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     title = {Integrable initial boundary value problems},
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Voir la notice de l'article provenant de la source Math-Net.Ru

The Korteweg–de Vries equation is considered on a half-line with zero boundary conditions at the origin and with arbitrary smooth initial values vanishing rapidly enough. The problem is effectively integrated by means of the inverse scattering method when the associated linear problem has no discrete spectrum. In this case the global solvability theorem is proved.