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

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Abstract

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.

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Acknowledgements

The authors express their sincere thanks to the referees and editors for their valuable comments. This work was supported by the National Natural Science Foundation of China (No. 11371326).

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Authors and Affiliations

  1. Normal School, Jinhua Polytechnic, Jinhua,  321007, Zhejiang, China

    Li Cheng

  2. Department of Mathematics, Zhejiang Normal University, Jinhua,  321004, Zhejiang, China

    Yi Zhang & Wen-Xiu Ma

  3. Department of Mathematical Sciences, International Institute for Symmetry Analysis and Mathematical Modelling, North-West University, Mafikeng Campus, Private Bag X2046, Mmabatho,  2735, South Africa

    Wen-Xiu Ma

  4. Department of Mathematics and Statistics, University of South Florida, Tampa, FL,  33620, USA

    Wen-Xiu Ma

  5. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao,  266590, Shandong, China

    Wen-Xiu Ma

Authors
  1. Li Cheng
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  2. Yi Zhang
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  3. Wen-Xiu Ma
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Correspondence to Li Cheng.

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Cheng, L., Zhang, Y. & Ma, WX. Pfaffians of B-type Kadomtsev–Petviashvili equation and complexitons to a class of nonlinear partial differential equations in (3\(+\)1) dimensions. Pramana - J Phys 93, 4 (2019). https://doi.org/10.1007/s12043-019-1752-0

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  • DOI: https://doi.org/10.1007/s12043-019-1752-0

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