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The Integrability of a New Fractional Soliton Hierarchy and Its Application

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  • Xiao-ming Zhu
  • Jian-bing Zhang
  • Yao Zhong Zhang

Abstract

Two fractional soliton equations are presented generated from the same spectral problem involved in a fractional potential by the zero-curvature representations. They are a kind of special reductions of the famous AKNS system. The two equations are integrable for they both possess explicit soliton solutions constructed by the N−fold Darboux transformation. As an application of the obtained solutions, new soliton solutions of the classic 2+1-dimensional Kadometsev-Petviashvili (KP) equation are soughed out by a cubic polynomial relation. Dynamic properties are analyzed in detail.

Suggested Citation

  • Xiao-ming Zhu & Jian-bing Zhang & Yao Zhong Zhang, 2022. "The Integrability of a New Fractional Soliton Hierarchy and Its Application," Advances in Mathematical Physics, Hindawi, vol. 2022, pages 1-14, May.
    • Handle: RePEc:hin:jnlamp:2200092
    DOI: 10.1155/2022/2200092
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    Cited by:

    1. Shou-Ting Chen & Wen-Xiu Ma, 2023. "Higher-Order Matrix Spectral Problems and Their Integrable Hamiltonian Hierarchies," Mathematics, MDPI, vol. 11(8), pages 1-9, April.

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