Traveling wave reduction of the resonant nonlinear Schrödinger equation with arbitrary refractive index is considered. The system of equations for real and imaginary parts is presented. The first integrals for the system of equations are found. This system of equations is transformed to the only governing nonlinear ordinary differential equations of the first order. Exact solutions in the form of periodic and solitary waves of this nonlinear ordinary differential equation are given for various values of the refractive index.

中文翻译：

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具有任意指数的谐振非线性Schrödinger方程的光学孤子

考虑了具有任意折射率的谐振非线性Schrödinger方程的行波减少。提出了实部和虚部方程组。找到方程组的第一个积分。该方程组被转换为唯一的一阶控制非线性常微分方程。针对各种折射率值，给出了该非线性常微分方程的周期波和孤立波形式的精确解。