Abstract Since the realization of Bose–Einstein condensates (BECs) trapped in optical potentials, intensive experimental and theoretical investigations have been carried out for bright and dark matter-wave solitons, coherent structures, modulational instability (MI), and nonlinear excitation of BEC matter waves, making them objects of fundamental interest in the vast realm of nonlinear physics and soft condensed-matter physics. Many of these states have their counterparts in optics, as concerns the nonlinear propagation of localized and extended light modes in the spatial, temporal, and spatiotemporal domains. Ubiquitous models, which are relevant to the description of diverse nonlinear media in one, two, and three dimensions (1D, 2D, and 3D), are provided by the nonlinear Schrodinger (NLS), alias Gross–Pitaevskii (GP), equations. In many settings, nontrivial solitons and coherent structures, which do not exist or are unstable in free space, can be created and/or stabilized by means of various management techniques, which are represented by NLS and GP equations with coefficients in front of linear or nonlinear terms which are functions of time and/or coordinates. Well-known examples are dispersion management in nonlinear fiber optics, and nonlinearity management in 1D, 2D, and 3D BEC. Developing this direction of research in various settings, efficient schemes of the spatiotemporal modulation of coefficients in the NLS/GP equations have been designed to engineer desirable robust nonlinear modes. This direction and related ones are the main topic of the present review. In particular, a broad and important theme is the creation and control of 1D matter-wave solitons in BEC by means of combination of the temporal or spatial modulation of the nonlinearity strength (which may be imposed by means of the Feshbach resonance induced by variable magnetic fields) and a time-dependent trapping potential. An essential ramification of this topic is analytical and numerical analysis of MI of continuous-wave (constant-amplitude) states, and control of the nonlinear development of MI. Another physically important topic is stabilization of 2D solitons against the critical collapse, driven by the cubic self-attraction, with the help of temporarily periodic nonlinearity management, which makes the sign of the nonlinearity periodically flipping. In addition to that, the review also includes some topics that do not directly include spatiotemporal modulation, but address physically important phenomena which demonstrate similar soliton dynamics. These are soliton motion in binary BEC, three-component solitons in spinor BEC, and dynamics of two-component 1D solitons under the action of spin–orbit coupling.

中文翻译：

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玻色-爱因斯坦凝聚中物质波孤子的时空工程

摘要 自从被困在光势中的玻色-爱因斯坦凝聚 (BECs) 实现以来，已经对亮和暗物质波孤子、相干结构、调制不稳定性 (MI) 和 BEC 物质的非线性激发进行了深入的实验和理论研究。波，使它们成为非线性物理学和软凝聚态物理学的广阔领域的基本兴趣对象。许多这些状态在光学中都有其对应物，因为涉及空间、时间和时空域中局部和扩展光模式的非线性传播。非线性薛定谔 (NLS)，别名 Gross-Pitaevskii (GP) 方程提供了无处不在的模型，这些模型与一维、二维和三维（1D、2D 和 3D）中的各种非线性介质的描述相关。在许多设置中，在自由空间中不存在或不稳定的非平凡孤子和相干结构可以通过各种管理技术来创建和/或稳定，这些技术由 NLS 和 GP 方程表示，其系数在线性或非线性项之前时间和/或坐标的函数。众所周知的例子是非线性光纤中的色散管理，以及 1D、2D 和 3D BEC 中的非线性管理。在各种设置中发展这一研究方向，NLS/GP 方程中系数的时空调制的有效方案已被设计为设计所需的鲁棒非线性模式。这个方向和相关的方向是本次审查的主要主题。特别是，一个广泛而重要的主题是通过结合非线性强度的时间或空间调制（可能通过可变磁场引起的 Feshbach 共振施加）在 BEC 中创建和控制一维物质波孤子和时间依赖的诱捕潜力。该主题的一个重要分支是连续波（恒定幅度）状态的 MI 的解析和数值分析，以及 MI 非线性发展的控制。另一个物理上重要的主题是在临时周期性非线性管理的帮助下，由三次自吸引驱动的 2D 孤子对临界坍缩的稳定性，这使得非线性的符号周期性地翻转。在此之上，审查还包括一些不直接包括时空调制的主题，但涉及展示类似孤子动力学的物理重要现象。这些是二元 BEC 中的孤子运动，自旋 BEC 中的三分量孤子，以及在自旋轨道耦合作用下的二分量一维孤子动力学。