Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
7154380 | Communications in Nonlinear Science and Numerical Simulation | 2019 | 19 Pages |
Abstract
In this work we derive families of explicit breather solutions of any order to the Kadomtsev-Petviashvili equation (KPI) and the Boussinesq equation. We employ the Hirota bilinear method combined with the KP hierarchy reduction method to determine these solutions. By taking a long wave limit of breather solutions, two types of semi-rational solutions to the KPI equation are constructed via using the determinant expression. The first type of semi-rational solutions only consists of breathers of arbitrary order and lumps of arbitrary order in the (x, y)-plane. The second type of semi-rational solutions comprises of solitons of arbitrary order, breathers of arbitrary order and lumps of arbitrary order in the (x, y)-plane.
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Authors
Wei Liu, Abdul-Majid Wazwaz, Xiaoxiao Zheng,