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The bound states of pure-high-even-order dispersion solitons

Author

Listed:
  • Li, Qi
  • Qiao, Feihong
  • Wen, Honglin
  • Li, Yingying
  • Zhou, Luyao
  • Wu, Ge
  • Liu, Lie
  • Gao, Bo

Abstract

Based on numerical methods and a variational approach, we investigate a generalized nonlinear Schrödinger equation containing only pure-high-even-order dispersion (PHEOD) and nonlinear terms. We find a family of the bound states of two PHEOD solitons and phenomenologically construct their mathematical expressions. Using these expressions and the system's Hamiltonian principle, we derive an analytical expression for the effective interaction potential between the two PHEOD solitons. This allows us to predict the equilibrium bound state of the two PHEOD solitons, a prediction subsequently verified by numerical simulations. We find that as the dispersion order increases, the depth of the potential well progressively decreases, and the position of its minimum moves toward zero. Furthermore, linear eigen-spectrum analysis of the bound state reveals a resonance instability. These findings provide crucial physical insights into the evolutionary dynamics of PHEOD soliton bound states.

Suggested Citation

  • Li, Qi & Qiao, Feihong & Wen, Honglin & Li, Yingying & Zhou, Luyao & Wu, Ge & Liu, Lie & Gao, Bo, 2026. "The bound states of pure-high-even-order dispersion solitons," Chaos, Solitons & Fractals, Elsevier, vol. 204(C).
    • Handle: RePEc:eee:chsofr:v:204:y:2026:i:c:s0960077925017552
    DOI: 10.1016/j.chaos.2025.117742
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