<p>This paper investigates wave dynamics of a (4+1)-dimensional variable-coefficient generalized Kadomtsev–Petviashvili equation. Within the framework of Bell polynomials, we derive its bilinear Bäcklund transformation and associated Lax pair, thereby establishing its integrability. Furthermore, by employing the Hirota method and the KP hierarchy reduction technique, we systematically construct a rich set of analytical solutions in Gram determinant form. These solutions include higher-order breathers, soliton–breather interaction phenomena, and higher-order rogue waves. We place particular emphasis on analyzing the dynamical behaviors of these solutions, with results demonstrating that the variable coefficients play a critical role in modulating the evolution patterns. This study provides significant insights into the complex dynamics of high-dimensional wave systems.</p>

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Higher-order breathers and rogue waves for a (4+1)-dimensional variable coefficient generalized Kadomtsev-Petviashvili equation in fluid dynamics and plasmas physics

  • Ai-Juan Hu,
  • Dun Zhao

摘要

This paper investigates wave dynamics of a (4+1)-dimensional variable-coefficient generalized Kadomtsev–Petviashvili equation. Within the framework of Bell polynomials, we derive its bilinear Bäcklund transformation and associated Lax pair, thereby establishing its integrability. Furthermore, by employing the Hirota method and the KP hierarchy reduction technique, we systematically construct a rich set of analytical solutions in Gram determinant form. These solutions include higher-order breathers, soliton–breather interaction phenomena, and higher-order rogue waves. We place particular emphasis on analyzing the dynamical behaviors of these solutions, with results demonstrating that the variable coefficients play a critical role in modulating the evolution patterns. This study provides significant insights into the complex dynamics of high-dimensional wave systems.