Burde G I
The Jacob Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Sede Boqer Campus, 84990, Israel.
Phys Rev E. 2020 Mar;101(3-2):036201. doi: 10.1103/PhysRevE.101.036201.
The authors of the paper "Shallow-water soliton dynamics beyond the Korteweg-de Vries equation" [1] write that they derived a new nonlinear equation describing shallow water gravity waves for an uneven bottom in the form of the higher (fifth)-order Korteweg-de Vries equation for surface elevation. The equation has been obtained by applying a perturbation method [2] for specific relations between the orders of the three small parameters of the problem α=O(β) and δ=O(β) up to the second order in β. In this comment, it is shown that the derivation presented in [1] is inconsistent because of an oversight concerning the orders of terms in equations of the Boussinesq system. Therefore the results, in particular, the new evolution equation and the dynamics that it describes, bear no relation to the problem under consideration. A consistent derivation is presented, and also results of applying the perturbation procedure with some other orderings between the small parameters are given to provide a broader view of the problem. Several new nonlinear evolution equations governing small amplitude shallow water waves for an uneven bottom have been derived.
论文《超越科特韦格 - 德弗里斯方程的浅水波孤子动力学》[1]的作者写道，他们推导了一个新的非线性方程，该方程以表面高程的高阶（第五阶）科特韦格 - 德弗里斯方程的形式描述了底部不平坦情况下的浅水波重力波。该方程是通过对问题的三个小参数的阶次之间的特定关系应用微扰方法[2]得到的，即α = O(β) 和δ = O(β)，直至β的二阶项。在本评论中，表明[1]中给出的推导是不一致的，因为在布辛涅斯克系统方程中对项的阶次存在疏忽。因此，其结果，特别是新的演化方程及其所描述的动力学，与所考虑的问题无关。本文给出了一个一致的推导，并且还给出了在小参数之间采用其他一些排序方式应用微扰过程的结果，以便更全面地看待该问题。已经推导了几个控制底部不平坦情况下小振幅浅水波的新的非线性演化方程。
