Duality family of KdV equation
Mathematical Physics
2023-01-16 v2 math.MP
Exactly Solvable and Integrable Systems
Abstract
It is revealed that there exist duality families of the KdV type equation. A duality family consists of an infinite number of generalized KdV (GKdV) equations. A duality transformation relates the GKdV equations in a duality family. Once a family member is solved, the duality transformation presents the solutions of all other family members. We show some dualities as examples, such as the soliton solution-soliton solution duality and the periodic solution-soliton solution duality.
Keywords
Cite
@article{arxiv.2301.00030,
title = {Duality family of KdV equation},
author = {Xin Gu and Yuan-Yuan Liu and Wen-Du Li and Wu-Sheng Dai},
journal= {arXiv preprint arXiv:2301.00030},
year = {2023}
}