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Lie Symmetries, qualitative analysis and exact solutions of nonlinear Schr'odinger equations with inhomogeneous nonlinearities

机译：Lie对称性，定性分析和非线性的精确解具有非齐次非线性的schr \“odinger方程

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Using Lie group theory and canonical transformations, we construct explicitsolutions of nonlinear Schrodinger equations with spatially inhomogeneousnonlinearities. We present the general theory, use it to study differentexamples and use the qualitative theory of dynamical systems to obtain someproperties of these solutions.

机译：使用李群理论和规范变换，我们构造了具有空间非均匀非线性的非线性薛定inger方程的显式解。我们提出了一般理论，用它来研究不同的例子，并使用动力学系统的定性理论来获得这些解的某些性质。

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Belmonte-Beitia, J.; Perez-Garcia, V. M.; Vekslerchik, V.; Torres, P. J.;
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年度 2008
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专利

1. Lie Symmetry Analysis and Exact Solutions to N -Coupled Nonlinear Schr?dinger's Equations with Kerr and Parabolic Law Nonlinearities [J] . Yakup Yildirim, Emrullah Yasar, Houria Triki, Romanian journal of physics . 2018,第1a2期

机译：具有Kerr和抛物线非线性的N耦合非线性薛定ding方程的Lie对称性分析和精确解。
2. Stationary solution of the nonlinear Schr?dinger's equation with log law nonlinearity by Lie symmetry analysis [J] . Biswas A., Khalique C.M. Waves in random and complex media . 2011,第4期

机译：李对数分析的对数律非线性的薛定ding方程的平稳解
3. Stationary solution of the nonlinear SchrÃ dinger's equation with log law nonlinearity by Lie symmetry analysis [J] . Anjan Biswas* Chaudry Masood Khalique Waves in Random and Complex Media . 2011,第4期

机译：李对数分析的对数律非线性的薛定er方程的平稳解
4. Localized nonlinear optical modes and the corresponding support structures: Exact solutions to the nonlinear Schrödinger equation with external potentials [C] . Malomed B. A., Stepanyants Y. A. 2010 International Conference on Electromagnetics in Advanced Applications . 2010

机译：局部非线性光学模式和相应的支撑结构：带外部电势的非线性薛定ding方程的精确解
5. Painleve analysis, Lie symmetries and integrability of nonlinear ordinary differential equations. [D] . Lu, Yixia. 2005

机译：非线性常微分方程的Painleve分析，Lie对称性和可积性。
6. Symmetry reduction and exact solutions of two higher-dimensional nonlinear evolution equations [O] . Yongyi Gu, Jianming Qi -1

机译：两个高维非线性发展方程的对称约化和精确解
7. Exact Solutions of the Two-Dimensional Discrete Nonlinear Schr"odinger Equation with Saturable Nonlinearity [O] . Khare, Avinash, Rasmussen, Kim Ø., Samuelsen, Mogens R., 2010

机译：二维离散非线性schr \“odinger的精确解具有可饱和非线性的方程

Lie Symmetries, qualitative analysis and exact solutions of nonlinear Schr'odinger equations with inhomogeneous nonlinearities

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