Abstract
In this paper, we consider (3 + 1)-dimensional Boiti-Leon-Manna-Pempinelli equation. Based on the bilinear form, we derive exact solutions of (3 + 1)-dimensional Boiti-Leon-Manna-Pempinelli (BLMP) equation by using the Wronskian technique, which include rational solutions, soliton solutions, positons and negatons.
Highlights
The Wronskian technique is introduced by Freeman and Nimmo [1]
Many researches are based on the Wronskian technique
We present the 1-soliton and 2-soliton solutions u1 2 x ln cosh 1 x 1 y 1 z 4 12t
Summary
The Wronskian technique is introduced by Freeman and Nimmo [1]. After that, many researches are based on the Wronskian technique. Where u u x, y,t and subscripts represent partial differentiation with respect to the given variable. This equation was used to describe the (2 + 1)-dimensional interaction of the Riemann wave propagated along the y-axis with a long wave propagated along the x-axis. The Painlevé analysis, Lax pairs, Bäcklund transformation, symmetry, similarity reductions and new exact solutions of the (2 + 1)-dimensional BLMP equation are given in [2,3,4]. In [5], based on the binary Bell polynomials, the bilinear form for the BLMP equation is obtained. New solutions of (2 + 1)-dimensional BLMP equation from Wronskian formalism and the Hirota method are obtained in [6,7]. Just by substituting u 2 ln f x, y, z,t into equation x (2), where the bilinear differential operator D is defined by Hirota [9] as
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