title: On the continuum limit for a semidiscrete Hirota equation.
abstract: In this paper, we propose a new semidiscrete Hirota equation which yields the Hirota equation in the continuum limit. We focus on the topic of how the discrete space stepδaffects the simulation for the soliton solution to the Hirota equation. The Darboux transformation and explicit solution for the semidiscrete Hirota equation are constructed. We show that the continuum limit for the semidiscrete Hirota equation, including the Lax pair, the Darboux transformation and the explicit solution, yields the corresponding results for the Hirota equation as [Formula: see text].
authors.affiliation: Área de Matemática Aplicada, ESCET , Universidad Rey Juan Carlos , C/ Tulipán s/n, 28933 Móstoles, Madrid, Spain.
authors.forename: Andrew
authors.initials: A
authors.lastname: Pickering
authors.affiliation: Department of Applied Mathematics , Shanghai University of International Business and Economics , 1900 Wenxiang Road, Shanghai 201620, People's Republic of China.
authors.forename: Hai-Qiong
authors.initials: HQ
authors.lastname: Zhao
authors.affiliation: School of Mathematical Sciences , Shanghai Jiao Tong University , 800 Dongchuan Road, Shanghai 200240, People's Republic of China.
authors.forename: Zuo-Nong
authors.identifier: 0000-0001-6369-7552
authors.initials: ZN
authors.lastname: Zhu
keywords: Darboux transformation; integrable discrete Hirota equation; soliton solutions