Multi-soliton solutions of KP equation with integrable boundary via partial differential -dressing method

[摘要] We construct by the use of partial differential -dressing method of Zakharov and Manakov new classes of exact multi-soliton solutions of the KP-1 and KP-2 versions of the Kadomtsev-Petviashvili equation with integrable boundary condition u(y)|(y=0) = 0. We satisfy exactly reality and boundary conditions for the field u(x, y, t) in the framework partial differential -dressing method and derive for exact solutions a general determinant formula in convenient form. As illustrations we present explicit examples of two-soliton solutions formed by two more simpler deformed one-solitons. The fulfillment of boundary condition in general case leads to the formation of corresponding multi-soliton solutions, i.e. to a certain nonlinear superpositions of an arbitrary number of pairs of bounded with each other one solitons. We interpret constructed multi-soliton solutions of the KP equation with integrable boundary as resonating eigenmodes of the field u(x, y, t) in the half-plane y >= 0 - an analogs of standing waves on the string with fixed end points. (c) 2021 Elsevier B.V. All rights reserved.

[发布日期] 2021-12-15

[关键词] Kadomtsev-Petviashvili equation;partial derivative-dressing method;Exact multi-soliton solutions;Integrable boundary condition