Abstract By means of standard Thomas–Fermi approximation, we present stable solutions of one- and two-dimensional (1D and 2D) multihump soliton structures, including 1D and 2D modulated solitons as well as 2D soliton clusters, supported by inhomogeneous defocusing nonlinear Kerr media. Such nonlinear settings may apply to nonlinear optics and Bose–Einstein condensates. All the 1D and 2D fundamental modes with different numbers of humps (for both modulated solitons and soliton clusters) are demonstrated to be robustly stable. Besides, the considered 2D nonlinear setting also supports a vast varieties of vortex modes—vortex soliton clusters. Such novel type of vortex soliton clusters is qualitatively different from the ordinary vortex clusters, on the account of the fact that the latter type is a single large soliton with several-vortex configurations inside it, while our predicted vortex clusters structures are composed of the arrays of unitary vortex solitons. Stability regions for all the soliton structures are identified via linear stability analysis and direct simulations.

中文翻译：

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纯非线性散焦介质中的调制孤子、孤子和涡旋簇

摘要 通过标准的 Thomas-Fermi 近似，我们提出了一维和二维（一维和二维）多峰孤子结构的稳定解，包括一维和二维调制孤子以及二维孤子簇，由非均匀散焦非线性克尔介质支持. 这种非线性设置可能适用于非线性光学和玻色-爱因斯坦凝聚。所有具有不同数量驼峰的一维和二维基模（对于调制孤子和孤子簇）都被证明是稳健稳定的。此外，所考虑的二维非线性设置还支持种类繁多的涡旋模式——涡旋孤子簇。这种新型涡孤子团与普通涡团有着质的不同，由于后一种类型是单个大孤子，内部具有多个涡旋结构，而我们预测的涡旋簇结构由单一涡旋孤子阵列组成。通过线性稳定性分析和直接模拟确定所有孤子结构的稳定区域。