Single soliton solution to the extended KdV equation over uneven depth

  • George Rowlands
  • Piotr RozmejEmail author
  • Eryk Infeld
  • Anna Karczewska
Open Access
Regular Article


In this note we look at the influence of a shallow, uneven riverbed on a soliton. The idea consists in an approximate transformation of the equation governing wave motion over an uneven bottom to an equation for a flat one for which the exact solution exists. The calculation is one space dimensional, and so corresponds to long trenches or banks under wide rivers or oceans.

Graphical abstract


Flowing matter: Nonlinear Physics 


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Copyright information

© The Author(s) 2017

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Authors and Affiliations

  • George Rowlands
    • 1
  • Piotr Rozmej
    • 2
    Email author
  • Eryk Infeld
    • 3
  • Anna Karczewska
    • 4
  1. 1.Department of PhysicsUniversity of WarwickCoventryUK
  2. 2.Institute of Physics, Faculty of Physics and AstronomyUniversity of Zielona GóraZielona GóraPoland
  3. 3.National Centre for Nuclear ResearchWarszawaPoland
  4. 4.Faculty of Mathematics, Computer Science and EconometricsUniversity of Zielona GóraZielona GóraPoland

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