Liouville soliton surfaces obtained using Darboux transformations
Exactly Solvable and Integrable Systems
2023-07-11 v2 Mathematical Physics
math.MP
Abstract
In this paper, Liouville soliton surfaces based on some soliton solutions of the Liouville equation are constructed and displayed graphically, including some of those corresponding to Darboux-transformed counterparts. We find that the Liouville soliton surfaces are centroaffine surfaces of Tzitzeica type and their centroaffine invariant can be expressed in terms of the Hamiltonian. The traveling wave solutions to Liouville equation from which these soliton surfaces stem are also obtained through a modified variation of parameters method which is shown to lead to elliptic functions solution method.
Keywords
Cite
@article{arxiv.2304.06885,
title = {Liouville soliton surfaces obtained using Darboux transformations},
author = {S. C. Mancas and K. R. Acharya and H. C. Rosu},
journal= {arXiv preprint arXiv:2304.06885},
year = {2023}
}
Comments
11 pages, 5 figures, 21 references, matches published version