This papers presents new exact analytical solutions of a generalized Ito equation having three nonlinear terms, third- and fifth-order derivative forms that model the dynamics of traveling waves in nonlinear dispersive systems. With the help of Riccati equation method, we obtain different kinds of exact traveling wave solutions containing dark, singular, trigonometric, rational and other form of waves solutions that are more general than classical ones existing in the literature. Despite the originality of the new results obtained, the method used here is very efficient, powerful and can be extended to other types of nonlinear equations and more. Moreover, the behaviors of traveling waves solutions are portrayed graphically by selecting suitable values for the physical parameters.

中文翻译：

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非线性色散系统中广义Ito方程的计算解

本文提出了广义 Ito 方程的新精确解析解，该方程具有三个非线性项、三阶和五阶导数形式，用于模拟非线性色散系统中的行波动力学。借助Riccati方程方法，我们得到了不同种类的精确行波解，包含暗波、奇异波、三角波、有理波等多种形式的波解，比现有文献中的经典波解更普遍。尽管获得的新结果具有独创性，但此处使用的方法非常有效、强大，并且可以扩展到其他类型的非线性方程等。此外，通过为物理参数选择合适的值，以图形方式描绘行波解的行为。