The Darboux Transformation for a New Fractional Schrödinger Equation Hierarchy

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

Advances in Mathematical Physics, 2024, vol. 2024, 1-13

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.

Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlamp:8898146

DOI: 10.1155/2024/8898146

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