The fourth-order nonlinear Schrödinger equation with four power nonlinearities is considered. The equation studied is the generalization of some well-known models and allows us to evaluate the influence various processes of pulse propagation. The main property of this equation is not integrability because the Cauchy problem for it cannot be solved by the inverse scattering transform. However this equation has some analytical solutions. Optical and embedded solitons corresponding to the considered mathematical model are given. Conservation laws of the partial differential equation for propagation pulses are found. Conservative quantities for the bright and embedded optical solitons are calculated.

中文翻译：

---

嵌入孤子四阶非线性薛定谔方程的精确解及守恒定律

考虑具有四次幂非线性的四阶非线性薛定谔方程。研究的方程是一些众所周知的模型的推广，使我们能够评估脉冲传播的各种过程的影响。该方程的主要性质不是可积性，因为它的柯西问题无法通过逆散射变换来解决。然而这个方程有一些解析解。给出了与所考虑的数学模型相对应的光学和嵌入式孤子。找到了传播脉冲偏微分方程的守恒定律。计算了亮光孤子和嵌入式光孤子的保守量。