This article is cited in 7 papers

Kadomtsev–Petviashvili Equation on the Half-Plane

E. V. Gudkova^a, I. T. Habibullin<sup>b

a</sup> Ufa State University of Oil and Technology
^b Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences

Abstract: 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, Lax pair, Marchenko equation, soliton.

Received: 20.11.2003

DOI: 10.4213/tmf89

 English version: Theoretical and Mathematical Physics, 2004, 140:2, 1086–1094

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