68 citations · 347 across the 41 of their papers we have counts for
41 papers
Solitary wave solutions, periodic and superposition solutions to the system of first-order (2+1)-dimensional Boussinesq's equations derived from the Euler equations for an ideal fluid model
Piotr Rozmej, Anna Karczewska
This article concludes the study of (2+1)-dimensional nonlinear wave equations that can be derived in a model of an ideal fluid with irrotational motion. In the considered case of…
(2+1)-dimensional KdV, fifth-order KdV, and Gardner equations derived from the ideal fluid model. Soliton, cnoidal and superposition solutions
Anna Karczewska, Piotr Rozmej
We study the problem of gravity surface waves for an ideal fluid model in the (2+1)-dimensional case. We apply a systematic procedure to derive the Boussinesq equations for a given…
Boussinesq's equations for (2+1)-dimensional gravity-surface waves in an ideal fluid model
Anna Karczewska, Piotr Rozmej
We study the problem of gravity surface waves for the ideal fluid model in (2+1)-dimensional case. We apply a systematic procedure for deriving the Boussinesq equations for a presc…
Inverted solutions of KdV-type and Gardner equations
Anna Karczewska, Piotr Rozmej
In most of the studies concerning nonlinear wave equations of Korteweg-de Vries type, the authors focus on waves of elevation. Such waves have general form ~$u_{\text{u}}(x,t)=A f(…
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]
Piotr Rozmej, Anna Karczewska
The authors of the paper "Two-dimensional third- and fifth-order nonlinear evolution equations for shallow water waves with surface tension" \cite{Fok} claim that they derived the…
Signatures of chaotic dynamics in wave motion according to the extended KdV equation
Anna Karczewska, Piotr Rozmej
In this communication we test the hypothesis that for some initial conditions the time evolution of surface waves according to the extended KdV equation (KdV2) exhibits signatures…