One‐ and two‐dimensional solitons of a multicomponent nonlocal nonlinear Schrödinger (NLS) system are constructed. The model finds applications in nonlinear optics, where it may describe the interaction of optical beams of different frequencies. We asymptotically reduce the model, via multiscale analysis, to completely integrable ones in both Cartesian and cylindrical geometries; we thus derive a Kadomtsev‐Petviashvili equation and its cylindrical counterpart, Johnson's equation. This way, we derive approximate soliton solutions of the nonlocal NLS system, which have the form of: (a) dark or antidark soliton stripes and (b) dark lumps in the Cartesian geometry, as well as (c) ring dark or antidark solitons in the cylindrical geometry. The type of the soliton, namely dark or antidark, is determined by the degree of nonlocality: dark (antidark) soliton states are formed for weaker (stronger) nonlocality. We perform numerical simulations and show that the derived soliton solutions do exist and propagate undistorted in the original nonlocal NLS system.

中文翻译：

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二维非局部非线性Schrödinger系统的多尺度展开向量孤子

构造了多分量非局部非线性薛定ding（NLS）系统的一维和二维孤子。该模型在非线性光学中找到了应用，可以描述不同频率的光束的相互作用。通过多尺度分析，我们渐近地将模型简化为笛卡尔几何和圆柱几何中的完全可积分模型。因此，我们推导了Kadomtsev-Petviashvili方程及其圆柱对应的Johnson方程。这样，我们得出非局部NLS系统的近似孤子解，其形式为：（a）笛卡尔几何中的暗或反暗孤子条纹和（b）暗块，以及（c）环形暗或反暗孤子在圆柱几何中。孤子的类型，即暗或反暗，取决于非局域程度：暗（反暗）孤子态是为较弱（更强）的非局部性而形成的。我们进行了数值模拟，结果表明导出的孤子解确实存在并且在原始的非局部NLS系统中不失真地传播。