Geodesic
Kadomtsev–Petviashvili Equation on the Half-Plane
Teoretičeskaâ i matematičeskaâ fizika, Tome 140 (2004) no. 2, pp. 230-240 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     title = {Kadomtsev{\textendash}Petviashvili {Equation} on the {Half-Plane}},
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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/

[1] P. G. Grinevich, P. M. Santini, The initial boundary value problems on the segment for the nonlinear Schrödinger equation; the algebro-geometric approach, I, E-print nlin.SI/0307026 | MR

[2] A. Degasperis, S. V. Manakov, P. M. Santini, TMF, 133:2 (2002), 184–201 | DOI | MR

[3] B. B. Kadomtsev, V. I. Petviashvili, DAN SSSR, 192:4 (1970), 753–756 | Zbl

[4] V. E. Zakharov, S. V. Manakov, S. P. Novikov, L. P. Pitaevskii, Teoriya solitonov. Metod obratnoi zadachi, Nauka, M., 1980 | MR

[5] V. E. Zakharov, A. B. Shabat, Funkts. analiz i ego prilozh., 8:3 (1974), 43–53 | MR | Zbl

[6] S. V. Manakov, Physica D, 3 (1981), 420–427 | DOI | MR | Zbl

[7] M. J. Ablowitz, D. Bar Yaacov, A. S. Fokas, Stud. Appl. Math., 69 (1983), 135–143 | DOI | MR | Zbl

[8] A. K. Pogrebkov, “KPII: new results and open problems”, Nonlinear Physics: Theoryand Experiment, Proc. of the Workshop (Gallipoli, Lecce, Italy, 27 June–6 July, 2002), eds. M. J. Ablowitz et al., World Scientific, Singapore, 2003, 108–117 | DOI | MR | Zbl

[9] I. T. Khabibullin, E. V. Gudkova, Funkts. analiz i ego prilozh., 38:2 (2004), 71–83 | DOI | MR | Zbl

[10] V. S. Dryuma, Pisma v ZhETF, 19:12 (1974), 753–755

[11] I. T. Habibullin, Multidimensional integrable boundary problems, E-print nlin.SI/0401028