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It is shown that the FEM gives a reasonable description of the wave dynamics of soliton waves governed by extended KdV equations. Some new results for several cases of bottom shapes are presented. The numerical scheme presented here is suitable for taking into account stochastic effects, which will be discussed in a subsequent paper.<\/jats:p>","DOI":"10.1515\/amcs-2016-0039","type":"journal-article","created":{"date-parts":[[2016,9,30]],"date-time":"2016-09-30T07:47:30Z","timestamp":1475221650000},"page":"555-567","source":"Crossref","is-referenced-by-count":7,"title":["A finite element method for extended KdV equations"],"prefix":"10.61822","volume":"26","author":[{"given":"Anna","family":"Karczewska","sequence":"first","affiliation":[{"name":"Faculty of Mathematics, Computer Science and Econometrics, University of Zielona G\u00f3ra, Szafrana 4a, 65-516 Zielona G\u00f3ra, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Piotr","family":"Rozmej","sequence":"additional","affiliation":[{"name":"Institute of Physics, Faculty of Physics and Astronomy, University of Zielona G\u00f3ra, Szafrana 4a, 65-516 Zielona G\u00f3ra, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Maciej","family":"Szczeci\u0144ski","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics, Computer Science and Econometrics, University of Zielona G\u00f3ra, Szafrana 4a, 65-516 Zielona G\u00f3ra, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bartosz","family":"Boguniewicz","sequence":"additional","affiliation":[{"name":"Institute of Physics, Faculty of Physics and Astronomy, University of Zielona G\u00f3ra, Szafrana 4a, 65-516 Zielona G\u00f3ra, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"37438","published-online":{"date-parts":[[2016,9,29]]},"reference":[{"key":"2021040704432802341_j_amcs-2016-0039_ref_001_w2aab2b8b9b1b7b1ab1ab1Aa","doi-asserted-by":"crossref","unstructured":"Ablowitz, M. and Segur, H. 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