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Advances in Mathematical Physics
Volume 2018, Article ID 5095482, 9 pages
Research Article

New Exact Superposition Solutions to KdV2 Equation

1Faculty of Physics and Astronomy, University of Zielona Góra, Szafrana 4a, 65-246 Zielona Góra, Poland
2Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, Szafrana 4a, 65-246 Zielona Góra, Poland

Correspondence should be addressed to Piotr Rozmej;

Received 27 September 2017; Revised 16 January 2018; Accepted 1 February 2018; Published 28 February 2018

Academic Editor: Antonio Scarfone

Copyright © 2018 Piotr Rozmej and Anna Karczewska. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


New exact solutions to the KdV2 equation (also known as the extended KdV equation) are constructed. The KdV2 equation is a second-order approximation of the set of Boussinesq’s equations for shallow water waves which in first-order approximation yields KdV. The exact solutions in the form of periodic functions found in the paper complement other forms of exact solutions to KdV2 obtained earlier, that is, the solitonic ones and periodic ones given by single or Jacobi elliptic functions.