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New Exact Superposition Solutions to KdV2 Equation

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  • Piotr Rozmej
  • Anna Karczewska

Abstract

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.

Suggested Citation

  • Piotr Rozmej & Anna Karczewska, 2018. "New Exact Superposition Solutions to KdV2 Equation," Advances in Mathematical Physics, Hindawi, vol. 2018, pages 1-9, February.
    • Handle: RePEc:hin:jnlamp:5095482
    DOI: 10.1155/2018/5095482
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