English

Polygons for finding exact solutions of nonlinear differential equations

Exactly Solvable and Integrable Systems 2007-05-23 v1

Abstract

New method for finding exact solutions of nonlinear differential equations is presented. It is based on constructing the polygon corresponding to the equation studied. The algorithms of power geometry are used. The method is applied for finding one -- parameter exact solutions of the generalized Korteveg -- de Vries -- Burgers equation, the generalized Kuramoto - Sivashinsky equation, and the fifth -- order nonlinear evolution equation. All these nonlinear equations contain the term umuxu^mu_x. New exact solitary waves are found.

Keywords

Cite

@article{arxiv.nlin/0601035,
  title  = {Polygons for finding exact solutions of nonlinear differential equations},
  author = {Nikolai A. Kudryashov and Maria V. Demina},
  journal= {arXiv preprint arXiv:nlin/0601035},
  year   = {2007}
}

Comments

16 pages, 2 figures

R2 v1 2026-07-22T18:14:52.923Z