Pfaffians of B-type Kadomtsev–Petviashvili equation and complexitons to a class of nonlinear partial differential equations in (3+1) dimensions

Pramana: Journal of physics

WEN-XIU MA^2,3,4,5²  YI ZHANG^2⁴  LI CHENG^1⁵ 

[1] College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, Shandong, China^5;Department of Mathematical Sciences, International Institute for Symmetry Analysis and Mathematical Modelling, North-West University, Mafikeng Campus, Private Bag X2046, Mmabatho 2735, South Africa^3;Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620, USA^4;Department of Mathematics, Zhejiang Normal University, Jinhua 321004, Zhejiang, China^2;Normal School, Jinhua Polytechnic, Jinhua 321007, Zhejiang, China^1

关键词: Generalised Kadomtsev–Petviashvili and B-type Kadomtsev–Petviashvili equations;    Pfaffian formulation;    sufficient conditions;    $N$-wave solutions;    complexitons;   

DOI  :  

学科分类：物理（综合）

来源: Indian Academy of Sciences

【 摘 要 】

The aim of this paper is to investigate a class of generalised Kadomtsev–Petviashvili (KP) and B-type Kadomtsev–Petviashvili (BKP) equations, which include many important nonlinear evolution equations as its special cases.By applying the fundamental Pfaffian identity, a general Pfaffian formulation is established and all the involved generating functions for Pfaffian entries need to satisfy a system of combined linear partial differential equations. The illustrative examples of the presented Pfaffian solutions are given for the (3+1)-dimensional generalised KP, Jimbo–Miwa and BKP equations. Moreover, we use the linear superposition principle to generate exponential travelling wave solutions and mixed resonant solutions of the considered equations.

【 授权许可】

CC BY