English

New exact superposition solutions to KdV2 equation

Fluid Dynamics 2018-04-09 v1

Abstract

New exact solutions to the KdV2 equation (known also 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 ~A2(\dn2[B(xvt),m]±m\cn[B(xvt),m]\dn[B(xvt),m])+D\frac{A}{2}\left(\dn^2[B(x-vt),m]\pm \sqrt{m}\,\cn [B(x-vt),m]\dn [B(x-vt),m]\right)+D~ in the form of periodic functions found in the paper complement other forms of exact solutions to KdV2 obtained earlier, i.e., the solitonic ones and periodic ones given by a single \cn2\cn^2 or \dn2\dn^2 Jacobi elliptic functions.

Keywords

Cite

@article{arxiv.1804.02222,
  title  = {New exact superposition solutions to KdV2 equation},
  author = {Piotr Rozmej and Anna Karczewska},
  journal= {arXiv preprint arXiv:1804.02222},
  year   = {2018}
}

Comments

20 pages, 16 figures

R2 v1 2026-06-23T01:15:57.186Z