Abstract
The authors of the paper "Shallowwater 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.
Original language  English 

Article number  036201 
Journal  Physical Review E 
Volume  101 
Issue number  3 
DOIs 

State  Published  1 Mar 2020 
ASJC Scopus subject areas
 Statistical and Nonlinear Physics
 Statistics and Probability
 Condensed Matter Physics