Riccati equation approach is used to look for exact travelling wave solutions of some nonlinear physical models. Solitary wave solutions are established for the modified KdV equation, the Boussinesq equation and the Zakharov-Kuznetsov equation. New generalized solitary wave solutions with some free parameters are derived. The obtained solutions, which includes some previously known solitary wave solutions and some new ones, are expressed by a composition of Riccati differential equation solutions followed by a polynomial. The employed approach, which is straightforward and concise, is expected to be further employed in obtaining new solitary wave solutions for nonlinear physical problems.

中文翻译：

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一些非线性物理模型的孤立波解使用 Riccati 方程方法

Riccati方程方法用于寻找一些非线性物理模型的精确行波解。分别为修正的KdV方程、Boussinesq方程和Zakharov-Kuznetsov方程建立了孤立波解。推导出具有一些自由参数的新的广义孤立波解。得到的解包括一些以前已知的孤立波解和一些新的解，由 Riccati 微分方程解的复合表示，后跟多项式。所采用的方法简单明了，有望进一步用于获得非线性物理问题的新孤立波解。