Nonlinear Waves

MONOGRAPHS

PREPRINTS

PUBLISHED PAPERS

  • Rozmej, P., Karczewska, A., "(2+1)-Dimensional Fifth-Order KdV Equation and (2+1)-Dimensional Gardner Equation Obtained from Ideal Fluid Model Revisited-Solitary Wave Solutions", Applied Sciences, Vol. 14,(16) 7094 (2024). DOI: 10.3390/app14167094

  • Karczewska, A., Rozmej, P., Kedziora, P., , "Comment on "Solitary Wave Solutions in (2+1) Dimensions: The KdV Equation Derived from Ideal Fluid Models", IJTP (2024) 63:105", International Journal of Theoretical Physics, Vol. 63, 272 (2024). DOI: 10.3390/app14167094

  • Rozmej, P., Karczewska, A., "Soliton, periodic and superposition solutions to nonlocal (2+1)-dimensional, extended KdV equation derived from the ideal fluid model", Nonlinear Dynamics, Vol. 111, 18373-18389 (2023). DOI: 10.1007/s11071-023-08819-7

  • Karczewska, A., Rozmej, P., "(2+1)-dimensional KdV, fifth-order KdV, and Gardner equations derived from the ideal fluid model. Soliton, cnoidal and superposition solutions", Communications in Nonlinear Science and Numerical Simulation, Vol. 125, 107317, (2023). DOI: 10.1016/j.cnsns.2023.107317

  • 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.

  • A. Karczewska, P. Rozmej, E. Infeld, G. Rowlands , "Adiabatic invariants of the extended KdV equation", Physics Letters A , 382 4(2017), 270-275.

  • 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).

  • 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.

  • 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).

  • 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.


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Last updated: June 11, 2025.