• 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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    • Keywords


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

    • 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.

    • Author Affiliations



      1. Normal School, Jinhua Polytechnic, Jinhua 321007, Zhejiang, China
      2. Department of Mathematics, Zhejiang Normal University, Jinhua 321004, Zhejiang, China
      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
      4. Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620, USA
      5. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, Shandong, China
    • Dates

  • Pramana – Journal of Physics | News

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