Geodesic
Kadomtsev--Petviashvili Equation on the Half-Plane
Teoretičeskaâ i matematičeskaâ fizika, Tome 140 (2004) no. 2, pp. 230-240

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We study the boundary value problem for the Kadomtsev–Petviashvili equation on the half-plane $y>0$ with a homogeneous condition along the boundary. We show that the problem can be efficiently solved using the dressing method. We present explicit solutions for particular cases of the boundary value problem.
Keywords: integrability, boundary conditions, Kadomtsev–Petviashvili equation
Mots-clés : Lax pair, Marchenko equation, soliton. 
@article{TMF_2004_140_2_a2,
     author = {E. V. Gudkova and I. T. Habibullin},
     title = {Kadomtsev--Petviashvili {Equation} on the {Half-Plane}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {230--240},
     publisher = {mathdoc},
     volume = {140},
     number = {2},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2004_140_2_a2/}
}
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E. V. Gudkova; I. T. Habibullin. Kadomtsev--Petviashvili Equation on the Half-Plane. Teoretičeskaâ i matematičeskaâ fizika, Tome 140 (2004) no. 2, pp. 230-240. http://geodesic.mathdoc.fr/item/TMF_2004_140_2_a2/