In this paper, we present a study of a fifth-order nonlinear partial differential equation, which was recently introduced in the literature. This equation can be used as a model for bidirectional water waves propagating in a shallow medium. Using elements of an optimal system of one-dimensional subalgebras, we perform similarity reductions culminating in analytic solutions. Rational, hyperbolic, power series and elliptic solutions are obtained. Furthermore, by using the multiple exponential function method we obtain one and two soliton solutions. Finally, local and low-order conserved quantities are derived by enlisting the multiplier approach.

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(1 + 1) 维五阶可积方程的守恒定律、经典对称性和精确解

在本文中，我们介绍了最近在文献中引入的五阶非线性偏微分方程的研究。该方程可以用作在浅层介质中传播的双向水波的模型。使用一维子代数的最优系统的元素，我们执行相似性减少，最终得到解析解。得到有理数、双曲线、幂级数和椭圆解。此外，通过使用多重指数函数方法，我们获得了一个和两个孤子解。最后，通过使用乘数方法导出局部和低阶守恒量。