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

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.

Automated summary

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.