• Infinitely-many conservation laws for two (2+1)-dimensional nonlinear evolution equations in fluids

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      https://www.ias.ac.in/article/fulltext/pram/083/01/0029-0037

    • Keywords

       

      Infinitely-many conservation laws; (2+1)-dimensional nonlinear evolution equations; Kadomtsev–Petviashvili equation; Davey–Stewartson equation; Lax pair; symbolic computation.

    • Abstract

       

      In this paper, a method that can be used to construct the infinitely-many conservation laws with the Lax pair is generalized from the (1+1)-dimensional nonlinear evolution equations (NLEEs) to the (2+1)-dimensional ones. Besides, we apply that method to the Kadomtsev– Petviashvili (KP) and Davey–Stewartson equations in fluids, and respectively obtain their infinitelymany conservation laws with symbolic computation. Based on that method, we can also construct the infinitely-many conservation laws for other multidimensional NLEEs possessing the Lax pairs, including the cylindrical KP, modified KP and (2+1)-dimensional Gardner equations, in fluids, plasmas, optical fibres and Bose–Einstein condensates.

    • Author Affiliations

       

      Yan Jiang1 2 Bo Tian1 2 Pan Wang1 2 Kun Su1 2

      1. State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876, China
      2. School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China
    • Dates

       
  • Pramana – Journal of Physics | News

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