Nonlinear Waves
MONOGRAPHS
Karczewska, A., Rozmej, P.,"Shallow water waves - extended Korteweg-de Vries equations". University of Zielona Gora (2018), 1-213. PDF-file.
SUBMITTED PAPERS
Karczewska, A., Rozmej, P., "The only true (2+1)-dimensional nonlocal KdV, fifth-order KdV, and
Gardner equations derived from the ideal fluid model", (2022).
PUBLISHED PAPERS
Karczewska, A., Rozmej, P., "Boussinesq's equations for (2+1)-dimensional surface gravity waves in an ideal fluid model,", Nonlinear Dynamics, Vol. 108, 4069-4080 (2022).
DOI: 10.1007/s11071-022-07385-8
Rozmej, P., Karczewska, A., "KdV, extended KdV, 5th-order KdV and Gardner equations generalized for uneven bottom versus corresponding Boussinesq's equations", Advances in Nonlinear Dynamics, Proceedings of the Second International Nonlinear Dynamics Conference (NODYCON 2021), Volume 3, 443-453 (2022). Springer International Publishing AG. DOI: 10.1007/978-3-030-81170-9
Karczewska, A., Rozmej, P., "Inverted solutions of KdV-type and Gardner equations", Acta Physica Polonica A, Vol. 140, no. 5, 445-449 (2021)
DOI: 10.12693/APhysPolA.140.445
Rozmej, P., Karczewska, A., "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]", Nonlinear Dynamics, Vol. 105, no. 5, 2855-2860 (2021) DOI: 10.1007/s11071-021-06716-5.
Karczewska, A., Rozmej P.,
"Can simple KdV-type equations be derived for shallow water
problem with bottom bathymetry?" Communications in Nonlinear Science and Numerical Simulations, Vol. 82 (2020), 105073. DOI: 10.1016/j.cnsns.2019.105073 .
Karczewska, A., Rozmej, P., "Generalized KdV-type equations versus Boussinesq's equations for uneven bottom - numerical study", Computational Methods in Science and Technology, Vol. 26, no. 4, 121-136 (2020) DOI: 10.12921/cmst.2020.0000036
Karczewska, A., Rozmej, P., "Remarks on existence/nonexistence of analytic solutions to higher order KdV equations", Acta Physica Polonica A, Vol. 136, no. 6, 910-915 (2019).
DOI: 10.12693/APhysPolA.136.910
Karczewska, A., Rozmej P.,
, "The new extended KdV equation for the case of an uneven bottom" Computational Methods in Science and Technology, Vol. 24 (4), (2018), pp. 221-225. DOI: 10.12921/cmst.2018.0000057 .
Rozmej P., Karczewska, A.
, "Adiabatic invariants of second order Korteweg - de Vries type equation" Chapter in: Nonlinear Systems, Vol. 1 : Mathematical Theory and Computation Methods, Springer, 2018, pp. 175-205. PDF-file .
Karczewska, A., Infeld E., Rowlands G., Rozmej P. , "Exact cnoidal solutions to the extended KdV equation", Acta Physica Polonica A, Vol. 133, No. 5, 1191-1199 (2018). DOI: 10.12693/APhysPolA.133.1191
Rozmej P., Karczewska A., "Exact superposition solutions to KdV2 equation" Advances in Mathematical Physics, vol. 2018, Article ID 5095482, 9 pages, (2018). DOI: 10.1155/2018/5095482.
Rozmej P., Karczewska A., Infeld E., "Superposition solutions to the extended KdV equation for water surface waves" Nonlinear Dynamics (2017), DOI 10.1007/s11071-017-3931-1.
Rowlands G, Rozmej P., Infeld E.,
Karczewska A., "Single soliton solution to the extended KdV equation over uneven depth", European Physical Journal E (2017) 40: 100, DOI 10.1140/epje/i2017-11591-7.
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A. Karczewska, P. Rozmej, E. Infeld, G. Rowlands , "Adiabatic invariants of the extended KdV equation", Physics Letters A , 382 4(2017), 270-275.
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A. Karczewska, P. Rozmej, M. Szczecinski, B. Boguniewicz,
"Finite element method for extended KdV equations", International Journal of Applied Mathematics and Computer Science, Vol. 26 (3), (2016).
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A. Karczewska, P. Rozmej, M. Szczecinski, B. Boguniewicz,
"Finite element method for stochastic extended KdV equations", Computational Methods in Physics and Technology, Vol. 22 (1) (2016), 19-29.
A. Karczewska, P. Rozmej, L. Rutkowski,
"Problems with energy of waves described by Korteweg de Vries equation", Annales Universitatis Mariae Curie-Sklodowska, Sectio AAA Physica, Vol. 70 (2015) 43-56.
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A. Karczewska, P. Rozmej, E. Infeld,
"Energy invariant for shallow water waves and the Korteweg -- de Vries equation. Doubts about the invariance of energy", Physical Review E 92, 053202 (2015).
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A. Karczewska, P. Rozmej, E. Infeld,
"Shallow water soliton dynamics beyond the Korteweg--de Vries equation", Physical Review E 90, 012907 (2014).
A. Karczewska, P. Rozmej, L. Rutkowski,
"A new nonlinear equation in the shallow water wave problem", Physica Scripta 89 5(2014).
PREPRINTS
Karczewska, A., Rozmej, P., "The only true (2+1)-dimensional nonlocal KdV, fifth-order KdV, and
Gardner equations derived from the ideal fluid model", Preprint: arXiv:2206.08964.
Karczewska, A., Rozmej, P., "Boussinesq's equations for (2+1)-dimensional gravity-surface waves in an ideal fluid model", Preprint: arXiv:2108.11150
.
Karczewska, A., Rozmej, P., "Inverted solutions of KdV-type and Gardner equations", Preprint: arXiv:2107.14237
.
Rozmej, P., Karczewska, A., "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]", Preprint: arXiv:2105.08519
.
Karczewska, A., Rozmej, P., "Signatures of chaotic dynamics in wave motion according to the extended KdV equation", Preprint: arXiv:2101.06632
.
Karczewska, A., Rozmej, P., "Generalized KdV-type equations versus Boussinesq's equations for uneven bottom - numerical study", Preprint: arXiv:2007.01267
.
Karczewska, A., Rozmej, P., "What kinds of KdV-type equations are allowed by an uneven bottom", Preprint: arXiv:1903.890.
Karczewska, A., Rozmej, P., " Remarks on existence/nonexistence of analytic solutions to higher order
KdV equations", Preprint: arXiv:1901.00001.
Rozmej, P., Karczewska, A., "Extended KdV equation for the case of uneven bottom", Preprint: arXiv:1810.07183.
Karczewska, A., Rozmej, P., "Comment on the paper "The third-order perturbed Korteweg-de Vries equation for shallow water waves with a non-flat bottom" by M. Fokou, T.C. Kofane, A. Mohamadou and E. Yomba, Eur. Phys. J. Plus, 132, 410 (2017)", Preprint: arXiv:1804.01940.
Rozmej P.
Karczewska A., Infeld E., "Superposition solutions to the extended KdV equation for water surface waves", Preprint: arXiv:1708.05975.
Infeld E.,
Karczewska A., Rozmej P., Rowlands G., "Solutions to the extended KdV equation for water surface waves", Preprint: arXiv:1612.03847.
Rowlands G, Rozmej P., Infeld E.,
Karczewska A., "Single soliton solution to the extended KdV equation over uneven depth", Preprint:arXiv:1612.05022.
Karczewska A., Rozmej P., Infeld E.,"Energy invariant for shallow water waves and the Korteweg -- de Vries equation. Is energy always an invariant". Preprint:
arXiv:1503.09089.
Karczewska A., Rozmej P., Infeld E.,"Shallow water soliton dynamics beyond KdV". Preprint:nlin.PS/1401.4859.
Karczewska A., Rozmej P., Rutkowski L.,"New nonlinear equation of KdV-type for a non-flat bottom".Preprint: nlin.PS/1401.4261.
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Last updated: June 22, 2022.