Two-dimensional third- and fifth-order nonlinear evolution equations for shallow water waves with surface tension

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 [1] consider the model of inviscid and incompressible fluid which motion is irrotational in a container with a flat bottom. In dimensional variables, the set of hydrodynamical equations has the following form: φ x x + φ yy + φ zz = 0, in the volume,…”

“…The authors take into account surface tension terms, as well. In this note, we neglect these terms since their presence or absence does not change the source of errors made in [1].…”

“…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.…”

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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.

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Analytic rogue wave solutions for a generalized fourth‐order Boussinesq equation in fluid mechanics

“…The research on the Boussinesq equation began in 1967 . Since then, a lot of works have developed on the Boussinesq equation and various Boussinesq‐type equations . Especially, the Boussinesq‐type equations have been applied to depict the nonlinear phenomena in ocean, coastal, harbor, and water engineering …”