Vortex solitons in the (2 + 1)-dimensional nonlinear Schr?dinger equation with variable diffraction and nonlinearity coefficients

Xu S.; Petrovi? N.Z.; Beli? M.R.

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Vortex solitons in the (2 + 1)-dimensional nonlinear Schr?dinger equation with variable diffraction and nonlinearity coefficients

机译：具有可变衍射和非线性系数的（2 +1）维非线性Schr？dinger方程中的涡旋孤子

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Using Hirota's bilinear method, we determine approximate analytical localized solutions of the (2 + 1)-dimensional nonlinear Schr?dinger equation with variable diffraction and nonlinearity coefficients. Our results indicate that a new family of vortices can be formed in the Kerr nonlinear media in the cylindrical geometry. Variable diffraction and nonlinearity coefficients allow utilization of the soliton management method. We present solitary solutions for two types of distributed coefficients: trigonometric and exponential. It is demonstrated that the soliton profiles found are structurally stable, but slowly expanding with propagation.

机译：使用Hirota的双线性方法，我们确定了具有可变衍射和非线性系数的（2 +1）维非线性Schr？dinger方程的近似解析局部解。我们的结果表明，可以在圆柱几何形状的Kerr非线性介质中形成一个新的涡旋族。可变的衍射系数和非线性系数允许使用孤子管理方法。我们提出两种类型的分布系数的孤立解：三角函数和指数函数。结果表明，所发现的孤子轮廓在结构上是稳定的，但随着传播而缓慢扩展。

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《Physica Scripta: An International Journal for Experimental and Theoretical Physics》 |2013年第4期|共8页
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Xu S.; Petrovi? N.Z.; Beli? M.R.;
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1. Vortex solitons in the (2 + 1)-dimensional nonlinear Schr?dinger equation with variable diffraction and nonlinearity coefficients [J] . Xu S., Petrovi? N.Z., Beli? M.R. Physica Scripta: An International Journal for Experimental and Theoretical Physics . 2013,第4期

机译：具有可变衍射和非线性系数的（2 +1）维非线性Schr？dinger方程中的涡旋孤子
2. Bilinear Forms and Dark-Dark Solitons for the Coupled Cubic-Quintic Nonlinear Schr(o)dinger Equations with Variable Coefficients in a Twin-Core Optical Fiber or Non-Kerr Medium [J] . Mei-Xia Chu, Bo Tian, Yu-Qiang Yuan, 理论物理通讯（英文版） . 2019,第012期

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3. Dynamics of solitons of the generalized (3+1)-dimensional nonlinear Schr(o)dinger equation with distributed coefficients [J] . Liu Xiao-Bei, Li Biao 中国物理：英文版 . 2011,第011期

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Vortex solitons in the (2 + 1)-dimensional nonlinear Schr?dinger equation with variable diffraction and nonlinearity coefficients

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