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The Darboux Transformation for a New Fractional Schrödinger Equation Hierarchy

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  • Xiao-ming Zhu
  • Jian-bing Zhang
  • Shou-ting Chen
  • Boris G. Konopelchenko

Abstract

It is well established that many integrable soliton equations can be constrained from the famous AKNS system. In this paper, aiming to generate new integrable soliton equations, the potentials of the AKNS system are constrained to a pair of fractional conjugate ones. The resulted equations include two fractional Scrödinger equations which are integrable for their own Lax pairs. Furthermore, odd-soliton solutions are obtained through N-fold Darboux transformations. Dynamic properties of the obtained solutions are analyzed in detail. These results suggest that the AKNS system allows a new type of potential constraints.PACS: 02.30.Ik, 05.45.Yv.

Suggested Citation

  • Xiao-ming Zhu & Jian-bing Zhang & Shou-ting Chen & Boris G. Konopelchenko, 2024. "The Darboux Transformation for a New Fractional Schrödinger Equation Hierarchy," Advances in Mathematical Physics, Hindawi, vol. 2024, pages 1-13, October.
    • Handle: RePEc:hin:jnlamp:8898146
    DOI: 10.1155/2024/8898146
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