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| 摘要: |
| 非局域非线性薛定谔方程可用来描述非线性光学、等离子体等方面的现象. 本文在双微分分次代数框架下推导了两类非局域非线性薛定谔方程. 通过该框架下的直接线性方法，利用非局域约化条件，在聚焦型与散焦型情形下构造了由Sylvester方程导出的精确解，并分别以若尔当块解和多孤子解等作为示例进行具体阐释. |
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| Abstract: |
| The nonlocal nonlinear Schr\"{o}dinger equation can be used to describe phenomena in nonlinear optics, plasmas, and related fields. In this paper, two types of nonlocal nonlinear Schr\"{o}dinger equations are derived under the framework of bidifferential graded algebras. By employing the direct linearization method under this framework and utilizing nonlocal reduction conditions, exact solutions derived from Sylvester equations are constructed for both focusing and defocusing cases. Specific illustrations, such as Jordan block solutions and multi-soliton solutions, are provided in detail. |
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