• Superposition behaviour between lump solutions and different forms of $N$-solitons ($N \rightarrow\infty$) for the fifth-order Korteweg–de Vries equation

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    • Keywords


      Fifth-orderKdVequation; lump solutions; superposition behaviour; soliton solutions; Hirota’s bilinear method

    • Abstract


      A lump-type solution of the (2 + 1)-dimensional generalised fifth-order Korteweg–de Vries (KdV) equation is obtained from the two-soliton solution by applying the parametric limit method. Some theorems and corollaries about the superposition behaviour between lump solutions and different forms of $N$-soliton ($N \rightarrow\infty$) solutions are constructed, and detailed proofs are given. Besides,we give a large number of examples and spatial evolution graphics to illustrate the effectiveness of the described theorems and corollaries. Some new nonlinear phenomena and superposition behaviour, such as rational-exponential type, rational-cosh-cos type, rational-sin type, rational-logarithmic type etc., are simulated and shown for the first time. Finally, we also illustrate the superposition between high-order lump-type solutions and $N$-soliton solutions.

    • Author Affiliations


      WEI TAN1 2 JUN LIU3

      1. Department of Mathematics, Sun Yat-sen University, Guangzhou 510275, China
      2. College of Mathematics and Statistics, Jishou University, Jishou 416000, China
      3. Institute of Applied Mathematics, Qujing Normal University, Qujing 655011, China
    • Dates

  • Pramana – Journal of Physics | News

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