Comment on Two-dimensional third-and fifth-order nonlinear evolution equations for shallow water waves with surface tension [Nonlinear Dyn, doi:10.1007/s11071-017-3938-7]

The authors of the paper Two-dimensional third-and fifth-order nonlinear evolution equations for shallow water waves with surface tension Fokou et al. (Nonlinear Dyn 91:1177-1189, 2018) claim that they derived the equation which generalizes the KdV equation to two space dimensions both in first and second order in small parameters. Moreover, they claim to obtain soliton solution to the derived first-order (2+1)-dimensional equation. The equation has been obtained by applying the perturbation method Burde (J Phys A: Math Theor 46:075501, 2013) for small parameters of the same order. The results, if correct, would be significant. In this comment, it is shown that the derivation presented in Fokou et al. (Nonlinear Dyn 91:1177-1189, 2018) is inconsistent because it violates fundamental properties of the velocity potential. Therefore, the results, particularly the new evolution equation and the dynamics that it describes, bear no relation to the problem under consideration.

Automated summary

The authors claim to have derived an equation generalizing the KdV equation to two space dimensions and obtained a soliton solution, but the derivation is shown to be inconsistent and the results have no relation to the problem under consideration.