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Analytic Investigation of a Generalized Variable-Coefficient KdV Equation with External-Force Term

Author

Listed:
  • Gongxun Li

    (LMIB and School of Mathematical Sciences, Beihang University, Beijing 100191, China)

  • Zhiyan Wang

    (LMIB and School of Mathematical Sciences, Beihang University, Beijing 100191, China)

  • Ke Wang

    (LMIB and School of Mathematical Sciences, Beihang University, Beijing 100191, China)

  • Nianqin Jiang

    (School of Physics, Beihang University, Beijing 100191, China)

  • Guangmei Wei

    (LMIB and School of Mathematical Sciences, Beihang University, Beijing 100191, China)

Abstract

This paper investigates integrable properties of a generalized variable-coefficient Korteweg–de Vries (gvcKdV) equation incorporating dissipation, inhomogeneous media, and an external-force term. Based on Painlevé analysis, sufficient and necessary conditions for the equation’s Painlevé integrability are obtained. Under specific integrability conditions, the Lax pair for this equation is successfully constructed using the extended Ablowitz–Kaup–Newell–Segur system (AKNS system). Furthermore, the Riccati-type Bäcklund transformation (R-BT), Wahlquist–Estabrook-type Bäcklund transformation (WE-BT), and the nonlinear superposition formula are derived. In utilizing these transformations and the formula, explicit one-soliton-like and two-soliton-like solutions are constructed from a seed solution. Moreover, the infinite conservation laws of the equation are systematically derived. Finally, the influence of variable coefficients and the external-force term on the propagation characteristics of a solitory wave is discussed, and soliton interaction is illustrated graphically.

Suggested Citation

  • Gongxun Li & Zhiyan Wang & Ke Wang & Nianqin Jiang & Guangmei Wei, 2025. "Analytic Investigation of a Generalized Variable-Coefficient KdV Equation with External-Force Term," Mathematics, MDPI, vol. 13(10), pages 1-15, May.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:10:p:1642-:d:1657966
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