The New Extended KdV Equation for the Case of an Uneven Bottom

• Autorzy: Karczewska A. , Rozmej P.

Identyfikatory

DOI

10.12921/cmst.2018.0000057

• Języki publikacji: EN

Abstrakty

EN

The consistent derivation of the extended KdV equation for an uneven bottom for the case of α = O(β) and δ = O(β 2 ) is presented. This is the only one case when second order KdV type nonlinear wave equation can be derived for arbitrary bounded bottom function.

Słowa kluczowe

EN

surface gravity waves; nonlinear equations; second order perturbation approach; uneven bottom

• Wydawca: Institute of Bioorganic Chemistry Scientific Publishers OWN, Polish Academy of Sciences
• Czasopismo: Computational Methods in Science and Technology
• Rocznik: 2018
• Tom: Vol. 24, No. 4
• Strony: 221--225
• Opis fizyczny: Bibliogr. 11 poz., rys.

Twórcy

autor

Karczewska A.

• Faculty of Mathematics, Computer Science and Econometrics University of Zielona Góra, Szafrana 4a, 65-246 Zielona Góra, Poland

autor

Rozmej P.

• Faculty of Physics and Astronomy University of Zielona Góra, Szafrana 4a, 65-246 Zielona Góra, Poland

Bibliografia

• [1] A. Karczewska, P. Rozmej, Ł. Rutkowski, A new nonlinear equation in the shallow water wave problem, Physica Scripta,89, 054026, (2014).
• [2] A. Karczewska, P. Rozmej, E. Infeld Shallow water soliton dynamics beyond KdV, Physical Review E, 90, 012907,(2014).
• [3] D.J. Korteweg, G. de Vries, On the change of form of the longwaves advancing in a rectangular canal, and on a new type of stationary waves, Phil. Mag. (5), 39, 422 (1895).
• [4] T.R. Marchant, N.F. Smyth, The extended Korteweg-de Vries equation and the resonant flow of a fluid over topography, Journal of Fluid Mechanics, 221, 263-288, (1990).
• [5] The review by the anonymous referee of the paper: P. Rozmej, A. Karczewska, Comment on the paper "The third-order perturbed Korteweg-de Vries equation for shallow water waves with a non-flat bottom" by M. T.C. Fokou Kofané, A. Mohamadou and E. Yomba, Eur. Phys. J. Plus, 132, 410 (2017), arXiv:1804.01940.
• [6] P. Rozmej, A. Karczewska, Extended KdV equation forthe case of uneven bottom, arXiv:1810.07183. Submitted to Phys. Rev. E.
• [7] E. Infeld, A. Karczewska, G. Rowlands, P. Rozmej, Exact cnoidal solutions of the extended KdV equation, Acta Phys. Pol. A, 133, 1191-1199, (2018).
• [8] P. Rozmej, A. Karczewska, E. Infeld: Superposition solutions to the extended KdV equation for water surface waves, Nonlinear Dynamics 91, 1085-1093, (2018).
• [9] P. Rozmej, A. Karczewska, New Exact Superposition Solutions to KdV2 Equation, Advances in Mathematical Physics.2018, Article ID 5095482, 1-9, (2018).
• [10] G. Rowlands, P. Rozmej, E. Infeld, A. Karczewska, Single soliton solution to the extended KdV equation over uneven depth, Eur. Phys. J. E, 40, 100, (2017).
• [11] A. Karczewska, P. Rozmej, Shallow water waves – extended Kortewed-de Vries equations, University of Zielona Góra, 2018.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).