Geodesic
An Initial-Boundary Value Problem on the Half-Line for the MKdV Equation
Funkcionalʹnyj analiz i ego priloženiâ, Tome 34 (2000) no. 1, pp. 65-75

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The initial-boundary value problem on the half-line for the modified Korteweg–de Vries equation with zero boundary conditions and arbitrary rapidly decaying initial conditions is embedded in the scheme of the inverse scattering method. The corresponding inverse scattering problem is reduced to the Riemann problem on a system of rays in the complex plane. 
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     author = {I. T. Habibullin},
     title = {An {Initial-Boundary} {Value} {Problem} on the {Half-Line} for the {MKdV} {Equation}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {65--75},
     publisher = {mathdoc},
     volume = {34},
     number = {1},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2000_34_1_a5/}
}
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I. T. Habibullin. An Initial-Boundary Value Problem on the Half-Line for the MKdV Equation. Funkcionalʹnyj analiz i ego priloženiâ, Tome 34 (2000) no. 1, pp. 65-75. http://geodesic.mathdoc.fr/item/FAA_2000_34_1_a5/