We introduce a model of media with the cubic attractive nonlinearity concentrated along a single or double stripe in the two-dimensional (2D) plane. The model can be realized in terms of nonlinear optics (in the spatial and temporal domains alike) and BEC. In recent works, it was concluded that search for stable 2D solitons in models with a spatially localized self-attractive nonlinearity is a challenging problem. We make use of the variational approximation (VA) and numerical methods to investigate conditions for the existence and stability of solitons in the present setting. The result crucially depends on the transverse shape of the stripe: while the rectangular profile supports stable 2D solitons, its smooth Gaussian-shaped counterpart makes all the solitons unstable. The double stripe with the rectangular profile admit stable solitons of three distinct types: symmetric and asymmetric ones with a single peak, and double-peak symmetric solitons. The shape and stability of single-peak solitons of either type are accurately predicted by the VA. Collisions between stable solitons are briefly considered too, by means of direct simulations. Depending on the relative velocity we observe excitation, decay or catastrophic self focusing.
Stabilization of Axisymmetric Airy Beams by Means of Diffraction and Nonlinearity Management in Two-Dimensional Fractional Nonlinear Schrödinger Equations
Solitons of the coupled Schrödinger - Korteweg - de Vries system with arbitrary strengths of the nonlinearity and dispersion
基于Zakharov耦合的薛定谔- Korteweg - de Vries（KdV）系统，对低频分量中任意的非线性和色散相对强度，得到了高频-低频耦合系统的新的双分量孤子解.复HF场由线性薛定谔方程控制，其中电势由实LF分量产生，而实LF分量又由KdV方程控制，KdV方程包括有质动力耦合项，表示HF场反馈到LF分量上。首先，我们通过直接模拟研究了脉冲形状脉冲的演化。在LF分量的色散弱于其非线性的情况下，输入产生几个孤子，其中HF分量比LF分量宽得多。在相反的情况下，该系统创建一个单独的孤子与两个组件的宽度近似相等。研究了稳定孤子间的碰撞，发现碰撞是非弹性的，较大的孤子会变得更强，较小的孤子会进一步衰减。在碰撞孤子中激发出鲁棒的本征模。一个新的家庭的近似解析的两个自由参数的两个组件孤子解被发现的LF组件的非线性和色散的任意相对强度，假设弱反馈的HF场到LF组件。此外，一个单参数（非通用）家庭的确切亮孤子的解决方案，与相互成比例的HF和LF组件，也产生。通过数值模拟，研究了由HF分量相对于LF分量的位移引起的双分量孤子的本征动力学，证明了一个鲁棒的本征模的激发
Collisions and fusion of one- and two-dimensional solitons driven by potential troughs in the cubic-quintic nonlinear Schrödinger equations
Guangzhou Maritime University（广州海事大学）；Shenzhen University（深圳大学）；Tel Aviv University（特拉维夫大学）；Horia Hulubei National Institute of Physics and Nuclear Engineering（霍里亚·胡卢贝伊国家物理与核工程研究所）
