流体中的3+1维广义B-型kadomtsev-Petviashvili方程的双线性自Bäcklund变换,振荡波解,呼吸子解和X-型孤子解

In this paper, a (3+1)-dimensional generalized B-type Kadomtsev-Petviashvili equation in a fluid, which is used to describe the long waves and has the application in water percolation, is investigated. Via the Hirota method, a bilinear auto-B?cklund transformation as well as shock-wave, breather and X-type soliton solutions are obtained. The shock waves and breathers are showed. The amplitudes and shapes of shock waves and breathers keep unchanged during the propagation. The X-type soliton on a periodic background are observed. The influence of the coefficients in the equation on the above waves are analysed.