An exact solution of partial differential equations provides a lot of information for a model. Since obtaining such answers is generally very difficult or in some cases impossible, having powerful analytical methods in determining them seems very necessary. Unlike numerical methods, these methods have fewer constraints such as stability, convergence, and approximation error. This paper aims to consider the generalized Schamel equation which arises in the modeling of some problems in plasma physics. Fortunately, by applying a new analytical method, a large number of exact solutions to the model are obtained. The structure used in the solutions specified in this method uses Jacobi elliptic functions. In another part of the paper, an effective numerical method, namely the reproducing kernel method is used to approximate the solutions of the equation. Numerical simulations of some acquired exact and approximate solutions are also included. It seems that the employed methods can be c...

中文翻译：

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广义Schamel方程的大量新的解析解和近似解。

偏微分方程的精确解为模型提供了很多信息。由于获得这样的答案通常非常困难，或者在某些情况下是不可能的，因此使用强大的分析方法确定这些答案似乎非常必要。与数值方法不同，这些方法具有较少的约束，例如稳定性，收敛性和逼近误差。本文旨在考虑在等离子体物理中一些问题的建模中出现的广义Schamel方程。幸运的是，通过应用新的分析方法，可以为模型获得大量精确的解。此方法指定的解决方案中使用的结构使用Jacobi椭圆函数。在本文的另一部分中，使用了一种有效的数值方法，即再生核方法来近似方程的解。还包括一些获得的精确解和近似解的数值模拟。看来所采用的方法可能是...