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M‐Lump Solution, Semirational Solution, and Self‐Consistent Source Extension of a Novel (2 + 1)‐Dimensional KdV Equation

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  • Rihan Hai
  • Hasi Gegen

Abstract

In this paper, we derive the M‐lump solution in terms of Matsuno determinant for the combined KP3 and KP4 (cKP3‐4) equation by applying the double‐sum identities for determinant and investigate the dynamical behaviors of 1‐ and 2‐lump solutions. In addition, we derive the Grammian solution for the cKP3‐4 equation and construct the semirational solutions from the Grammian solution. Through the asymptotic analysis, we show that the semirational solutions describe fusion and fission of lumps and line solitons and rogue lump phenomena. Furthermore, we construct the cKP3‐4 equation with self‐consistent sources via the source generation procedure and present its Grammian and Wronskian solution.

Suggested Citation

  • Rihan Hai & Hasi Gegen, 2022. "M‐Lump Solution, Semirational Solution, and Self‐Consistent Source Extension of a Novel (2 + 1)‐Dimensional KdV Equation," Advances in Mathematical Physics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jnlamp:v:2022:y:2022:i:1:n:8105654
    DOI: 10.1155/2022/8105654
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    References listed on IDEAS

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    1. Zhang, Yi & Sun, YanBo & Xiang, Wen, 2015. "The rogue waves of the KP equation with self-consistent sources," Applied Mathematics and Computation, Elsevier, vol. 263(C), pages 204-213.
    2. Lin, Runliang & Zeng, Yunbo & Ma, Wen-Xiu, 2001. "Solving the KdV hierarchy with self-consistent sources by inverse scattering method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 291(1), pages 287-298.
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