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Nonlocal KdV hierarchy reduction and asymptotic solutions in the nonlocal Lakshmanan–Porsezian–Daniel equation

Author

Listed:
  • Li, Wentao
  • Zhang, Zhao
  • Yang, Xiangyu
  • Li, Biao

Abstract

The nonlocal Lakshmanan–Porsezian–Daniel (LPD) equation with higher-order dispersion and nonlinear effects is investigated. By employing the multiple-scale method, the nonlocal Korteweg–de Vries (KdV) hierarchy, which admits only PT-symmetric invariant solutions, has been derived from the reverse space–time nonlocal LPD equation. The one- and two-soliton solutions of the nonlocal KdV equation accurately reproduce the corresponding soliton dynamics of the nonlocal LPD equation, while the nonlocal fifth-order KdV term provides essential higher-order dispersion corrections. The remaining discrepancies arise mainly from differences in the higher-order perturbation terms between the nonlocal LPD and KdV equations, suggesting that the fitting accuracy can be further improved by incorporating additional higher-order corrections.

Suggested Citation

  • Li, Wentao & Zhang, Zhao & Yang, Xiangyu & Li, Biao, 2026. "Nonlocal KdV hierarchy reduction and asymptotic solutions in the nonlocal Lakshmanan–Porsezian–Daniel equation," Chaos, Solitons & Fractals, Elsevier, vol. 206(C).
    • Handle: RePEc:eee:chsofr:v:206:y:2026:i:c:s0960077926001232
    DOI: 10.1016/j.chaos.2026.117982
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