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Kadomtsev-Petviashvili equation on the half-plane. (English) Zbl 1178.35319
Theor. Math. Phys. 140, No. 2, 1086-1094 (2004); translation from Teor. Mat. Fiz. 140, No. 2, 230-240 (2004).
Summary: 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.

MSC:
35Q51 Soliton equations
35Q53 KdV equations (Korteweg-de Vries equations)
37K15 Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems
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