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$\bar{\partial}$ $\bar{\partial}$ -Dressing method for a generalized Hirota equation

Yehui Huang

https://orcid.org/0000-0003-1269-724X

School of Mathematics and Physics, North China Electric Power University, Beijing 102206, P. R. China

E-mail Address: yhhuang@ncepu.edu.cn

Corresponding author.

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Jingjing Di

School of Mathematics and Physics, North China Electric Power University, Beijing 102206, P. R. China

E-mail Address: jjingdi@163.com

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, and

Yuqin Yao

Department of Applied Mathematics, China Agricultural University, Beijing 100083, P. R. China

E-mail Address: yyqinw@126.com

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https://doi.org/10.1142/S0217979222501119Cited by:4 (Source: Crossref)

Abstract

Based on a $2 \times 2$ $2 \times 2$ matrix $\bar{\partial}$ $\bar{\partial}$ problem, we have obtained the Lax pair by constructing a spectral transformation matrix. The Hirota equation with self-consistent sources is derived by considering the nonanalytic part of the dispersion relation. Furthermore, explicit solutions including N-soliton solutions are computed by $\bar{\partial}$ $\bar{\partial}$ -dressing method, and N-soliton solutions of the Hirota equation with self-consistent sources are obtained by using the properties of Cauchy matrix. The dynamic behavior of soliton solutions is analyzed.

Keywords:

PACS: 02.30.IK

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