English

Representations and classification of traveling wave solutions to Sinh-G{\"o}rdon equation

Exactly Solvable and Integrable Systems 2015-05-13 v1 Pattern Formation and Solitons

Abstract

Two concepts named atom solution and combinatory solution are defined. The classification of all single traveling wave atom solutions to Sinh-G{\"o}rdon equation is obtained, and qualitative properties of solutions are discussed. In particular, we point out that some qualitative properties derived intuitively from dynamic system method aren't true. In final, we prove that our solutions to Sinh-G{\"o}rdon equation include all solutions obtained in the paper[Fu Z T et al, Commu. in Theor. Phys.(Beijing) 2006 45 55]. Through an example, we show how to give some new identities on Jacobian elliptic functions.

Keywords

Cite

@article{arxiv.0706.1673,
  title  = {Representations and classification of traveling wave solutions to Sinh-G{\"o}rdon equation},
  author = {Cheng-shi Liu},
  journal= {arXiv preprint arXiv:0706.1673},
  year   = {2015}
}

Comments

12 pages. accepted by Communications in theoretical physics (Beijing)