This paper employs the new robust solver to retrieve exact solutions to a Kaup–Newell model equation and the nonlinear coupled Konno–Oono equation. This solver yields the closed formula for the solutions. Different types of travelling wave solutions, i.e., rational function, hyperbolic function and trigonometric function solutions with many capricious parameters are revealed. Subsequently, by utilizing Matlab 18 we plot 2D and 3D surfaces of obtained analytical solutions for suitable values of the free parameters. The depiction of the solver is direct, vital, sturdy and can be applied to other nonlinear partial differential equations. We also show that some proposed rational solutions can be rapprochement with some known probability distributions.

本文采用了新的鲁棒求解器来检索Kaup-Newell模型方程和非线性耦合Konno-Oono方程的精确解。该求解器得出解决方案的封闭式。揭示了不同类型的行波解，即具有许多可变参数的有理函数，双曲函数和三角函数解。随后，通过使用Matlab 18，我们绘制了获得的分析溶液的2D和3D表面，以获取自由参数的合适值。解算器的描述是直接的，至关重要的，坚固的，并且可以应用于其他非线性偏微分方程。我们还表明，一些提出的有理解可以和一些已知的概率分布进行和解。