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The integrability, equivalence and solutions of two kinds of integrable deformed fourth-order matrix NLS equations

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Abstract

Based on the higher-order restricted flows, the first type of integrable deformed fourth-order matrix NLS equations, that is, the fourth-order matrix NLS equations with self-consistent sources (FMNLSSCS), is derived. By virtue of the \({\bar{\partial }}\)-dressing method, the second type of integrable deformed fourth-order matrix NLS equations called the fourth-order matrix NLS–Maxwell–Bloch system (FMNLS-MB) is presented. We prove the equivalence of the FMNLSSCS and the FMNLS-MB successfully. Furthermore, N-soliton solutions are explicitly obtained by means of the Cauchy matrix method starting from corresponding Sylvester equation.

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Funding

Yuqin Yao was supported by National Natural Science Foundation of China (Grant. No. 12171475).

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  1. College of Science, China Agricultural University, Beijing, 100083, People’s Republic of China

    Yuqin Yao, Hui Zhou & Fei Li

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  1. Yuqin Yao
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Yao, Y., Zhou, H. & Li, F. The integrability, equivalence and solutions of two kinds of integrable deformed fourth-order matrix NLS equations. Nonlinear Dyn 111, 8673–8685 (2023). https://doi.org/10.1007/s11071-023-08275-3

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