@article{Zhao2023, 
author = {Qiulan Zhao and Muhammad Arham Amin and Xinyue Li},
title = {Classical Darboux transformation and exact soliton solutions of a two-component complex short pulse equation},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {4},
pages = {8811-8828},
keywords = {integrability, hodograph transformation, Darboux transformation, exact soliton solutions},
url = {https://www.sciopen.com/article/10.3934/math.2023442},
doi = {10.3934/math.2023442},
abstract = {This paper investigates soliton solutions to a two-component complex short pulse (c-SP) equation. Based on the known Lax pair representation of this equation, we verify the integrability of a two-component c-SP equation and find an equivalent convenient Lax pair through hodograph transformation. The classical Darboux transformation (DT) is utilized to construct multi-soliton solutions for the two-component c-SP equation as an ordinary determinant. Furthermore, the details of one-soliton and two-soliton solutions are presented and generalized for    N-fold soliton solutions. We also derive exact soliton solutions in explicit form using suitable reduction constraints from various "seed" solutions and explore them via graphs.}
}