4.7 Article

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

期刊

NONLINEAR DYNAMICS
卷 111, 期 9, 页码 8673-8685

出版社

SPRINGER
DOI: 10.1007/s11071-023-08275-3

关键词

Higher-order restricted flows; partial derivative-dressing method; Fourth-order matrix NLS equation; Cauchy matrix method; Soliton solution

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Based on higher-order restricted flows, the first type of integrable deformed fourth-order matrix NLS equations, called FMNLSSCS, is derived. By using the partial derivative-dressing method, the second type of integrable deformed fourth-order matrix NLS equations, called FMNLS-MB, is presented. The equivalence between FMNLSSCS and FMNLS-MB is successfully proved and N-soliton solutions are obtained explicitly using the Cauchy matrix method.
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 partial derivative-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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