Pfaffian solution for dark-dark soliton to the coupled complex modified Korteweg-de Vries equation
Mathematical Physics
2025-03-18 v1 math.MP
Exactly Solvable and Integrable Systems
Abstract
In this paper, we study coupled complex modified Korteweg-de Vries (ccmKdV) equation by combining the Hirota's method and the Kadomtsev-Petviashvili (KP) reduction method. First, we show that the bilinear form of the ccmKdV equation under nonzero boundary condition is linked to the discrete BKP hierarchy through Miwa transformation. Based on this finding, we construct the dark-dark soliton solution in the pfaffian form. The dynamical behaviors for one- and two-soliton are analyzed and illustrated.
Keywords
Cite
@article{arxiv.2503.12740,
title = {Pfaffian solution for dark-dark soliton to the coupled complex modified Korteweg-de Vries equation},
author = {Chenxi Li and Xiaochuan Liu and Bao-Feng Feng},
journal= {arXiv preprint arXiv:2503.12740},
year = {2025}
}