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Soliton, breather and rogue wave solutions of the nonlinear Schrödinger equation via Darboux transformation on a time–space scale

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  • Sang, Xue
  • Dong, Huanhe
  • Fang, Yong
  • Liu, Mingshuo
  • Kong, Yuan

Abstract

Solving soliton equations on the time–space scale has always been a challenging issue. In this paper, we firstly generalize the Ablowitz–Kaup–Newel–Segur (AKNS) method to the time–space scale, concurrently obtain the nonlinear Schrödinger (NLS) equation on this scale, which unifies the continuous and the semi-discrete NLS equations. On this basis, the N-fold Darboux transformation is proposed for the NLS equation on a space scale. As applications, soliton, breather, and rogue wave solutions of NLS equation are derived from diverse seed solutions on a space scale. Specially, the rouge solution on a space scale is obtained for the first time.

Suggested Citation

  • Sang, Xue & Dong, Huanhe & Fang, Yong & Liu, Mingshuo & Kong, Yuan, 2024. "Soliton, breather and rogue wave solutions of the nonlinear Schrödinger equation via Darboux transformation on a time–space scale," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    • Handle: RePEc:eee:chsofr:v:184:y:2024:i:c:s0960077924006040
    DOI: 10.1016/j.chaos.2024.115052
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    References listed on IDEAS

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    1. Yuan, Cuilian & Yang, Hujiang & Meng, Xiankui & Tian, Ye & Zhou, Qin & Liu, Wenjun, 2023. "Modulational instability and discrete rogue waves with adjustable positions for a two-component higher-order Ablowitz–Ladik system associated with 4 × 4 Lax pair," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    2. Shen, Yuan & Tian, Bo & Zhou, Tian-Yu & Gao, Xiao-Tian, 2022. "Nonlinear differential-difference hierarchy relevant to the Ablowitz-Ladik equation: Lax pair, conservation laws, N-fold Darboux transformation and explicit exact solutions," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    3. Sun, Zhuo-Yue & Deng, Duo & Pang, Zhao-Guang & Yang, Zhen-Jun, 2024. "Nonlinear transmission dynamics of mutual transformation between array modes and hollow modes in elliptical sine-Gaussian cross-phase beams," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    4. D. R. Solli & C. Ropers & P. Koonath & B. Jalali, 2007. "Optical rogue waves," Nature, Nature, vol. 450(7172), pages 1054-1057, December.
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