This article offers a review of (chiefly, theoretical) results for self-trapped states (solitons) in two- and three-dimensional (2D and 3D) models of nonlinear dissipative media. The existence of such solitons requires to maintain two stable balances: between nonlinear self-focusing and linear spreading (diffraction and/or dispersion) of the physical fields, and between losses and gain in the medium. Due to the interplay of these conditions, dissipative solitons exist, unlike solitons in conservative models, not in continuous families, but as isolated solutions (attractors). The main issue in the theory is stability of multidimensional dissipative solitons, especially ones with embedded vorticity. First, stable 2D dissipative solitons are presented in the framework of the complex Ginzburg–Landau equation with the cubic–quintic nonlinearity, which combines linear loss, cubic gain, and quintic loss (the linear loss is necessary to stabilize zero background around dissipative solitons, while the quintic loss provides for the global stability of the setting). In addition to fundamental (zero-vorticity) solitons, stable spiral solitons produced by the CGL equation are produced too, with intrinsic vorticities $S=1$ and 2. Stable 2D solitons were also found in a system built of two linearly-coupled optical fields, with linear gain acting in one and linear loss, which plays the stabilizing role, in the other. In this case, the inclusion of the cubic loss (without quintic terms) is sufficient for the creation of stable fundamental and vortical dissipative solitons in the linearly-coupled system. In addition to truly localized states, weakly localized ones are presented too, in the single-component model with nonlinear losses, which does not include explicit gain. In that case, the losses are compensated by the influx of power from the reservoir provided, at the spatial infinity, by the weakly localized structure of the solution. Other classes of 2D models which are considered in this review make use of spatially modulated loss or gain to predict many species of robust dissipative solitons, including localized dynamical states featuring complex periodically recurring metamorphoses. Stable fundamental and vortical solitons are also produced by models including a trapping or spatially periodic potential. In the latter case, the consideration addresses 2D gap dissipative solitons as well. 2D two-component dissipative models including spin–orbit coupling are considered too. They give rise to stable states in the form of semi-vortex solitons, with vorticity carried by one component. In addition to the 2D solitons, the review includes 3D fundamental and vortical dissipative solitons, stabilized by the cubic–quintic nonlinearity and/or external potentials. Collisions between 3D dissipative solitons are considered too.

本文回顾了非线性耗散介质的二维和三维（2D 和 3D）模型中自陷态（孤子）的（主要是理论）结果。这种孤子的存在需要保持两个稳定的平衡：在物理场的非线性自聚焦和线性扩展（衍射和/或色散）之间，以及在介质中的损耗和增益之间。由于这些条件的相互作用，耗散孤子存在，与保守模型中的孤子不同，它不在连续族中，而是作为孤立的解（吸引子）。理论中的主要问题是多维耗散孤子的稳定性，尤其是具有嵌入涡度的孤子. 首先，在具有三次-五次非线性的复杂 Ginzburg-Landau 方程的框架中呈现稳定的二维耗散孤子，该方程结合了线性损耗、三次增益和五次损耗（线性损耗对于稳定耗散孤子周围的零背景是必要的，而五次损失提供了设置的全局稳定性）。除了基本（零涡度）孤子外，还产生了由 CGL 方程产生的稳定螺旋孤子，具有固有涡度$\mathrm{小号}=1$2. 在由两个线性耦合光场构成的系统中也发现了稳定的二维孤子，其中一个具有线性增益，另一个具有稳定作用的线性损耗。在这种情况下，包含三次损耗（没有五次项）足以在线性耦合系统中创建稳定的基本和涡旋耗散孤子。除了真正的局部化状态外，在具有非线性损耗的单分量模型中也呈现了弱局部化状态，其中不包括显式增益。在这种情况下，通过溶液的弱局部结构，在空间无穷大的情况下，来自水库的能量流入可以补偿损失。本综述中考虑的其他类型的 2D 模型利用空间调制的损失或增益来预测许多种类的鲁棒耗散孤子，包括具有复杂周期性重复变质的局部动态状态。包括捕获或空间周期性势的模型也产生稳定的基本和涡旋孤子。在后一种情况下，考虑解决 2D间隙耗散孤子也是如此。还考虑了包括自旋轨道耦合在内的二维二分量耗散模型。它们以半涡孤子的形式产生稳定状态，涡量由一个分量携带。除了 2D 孤子之外，该评论还包括 3D 基本和涡旋耗散孤子，由三次-五次非线性和/或外部电位稳定。3D 耗散孤子之间的碰撞也被考虑在内。