Abstract
In this paper we study a -dimensional generalized B-type Kadomtsev-Petviashvili (BKP) equation. This equation is an extension of the well-known Kadomtsev-Petviashvili equation, which describes weakly dispersive and small amplitude waves propagating in quasi-two-dimensional media. We first obtain exact solutions of the BKP equation using the multiple-exp function and simplest equation methods. Furthermore, the conservation laws for the BKP equation are constructed by using the multiplier method.
Highlights
1 Introduction It is well known that many phenomena in science and engineering, especially in fluid mechanics, solid state physics, plasma physics, plasma waves and biology, are described by the nonlinear partial differential equations (NLPDEs)
The investigation of exact solutions of NLPDEs plays an important role in the study of NLPDEs
The purpose of this paper is to study one such NLPDE, namely the ( + )-dimensional generalized B-type Kadomtsev-Petviashvili (BKP) equation, that is given by [ ]
Summary
It is well known that many phenomena in science and engineering, especially in fluid mechanics, solid state physics, plasma physics, plasma waves and biology, are described by the nonlinear partial differential equations (NLPDEs). The purpose of this paper is to study one such NLPDE, namely the ( + )-dimensional generalized B-type Kadomtsev-Petviashvili (BKP) equation, that is given by [ ] The ( + )dimensional nonlinear generalized BKP equation uyt – uxxxy – (uxuy)x + ( uxx + uzz) = , In [ ] a new form of the ( + )dimensional BKP equation given by
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