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Canonical solution and singularity propagations of the nonlocal semi-discrete Schrödinger equation

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Abstract

In this paper, a nonlocal semi-discrete Schrödinger equation is first reduced from the combined Ragnisco–Tu equation with a nonlocal reduction, which is connected to the reverse-t Schrödinger equation and the reverse-(x, t) Schrödinger equation under two proper continuum limits, respectively. We derive the constrained double Wronskian solution of the nonlocal semi-discrete Schrödinger equation, by putting a constraint with a group of algebra equations on the double Wronskian solution of the unreduced equation. We further construct the canonical form of the constrained double Wronskian solution with the help of the Jordan decomposition and the invariance property of the constrained double Wronskian solution under similarity transformations of matrixes. Finally, in complex field, a complete classification of the spectral parameter k in soliton is made, which allows us to analyse singularity points of soliton, and describe the related singularity propagations in figures.

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  1. Research Center for Fintech, Zhejiang Lab, Hangzhou, 311121, People’s Republic of China

    Kui Chen, Chongning Na & Jiaxi Yang

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  1. Kui Chen
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Chen, K., Na, C. & Yang, J. Canonical solution and singularity propagations of the nonlocal semi-discrete Schrödinger equation. Nonlinear Dyn 111, 1685–1700 (2023). https://doi.org/10.1007/s11071-022-07912-7

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