Open AccessInverse scattering transform and soliton solutions of an integrable nonlocal Hirota equation
Author(s) -
Yuan Li,
ShouFu Tian
Publication year - 2021
Publication title -
communications on pure and applied analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.077
H-Index - 42
eISSN - 1553-5258
pISSN - 1534-0392
DOI - 10.3934/cpaa.2021178
Subject(s) - inverse scattering transform , inverse scattering problem , soliton , integrable system , scattering , mathematical analysis , lax pair , space (punctuation) , mathematical physics , scattering theory , mathematics , quantum inverse scattering method , physics , inverse , sine gordon equation , inverse problem , quantum mechanics , nonlinear system , linguistics , philosophy , geometry
In this work, we study the inverse scattering transform of a nonlocal Hirota equation in detail, and obtain the corresponding soliton solutions formula. Starting from the Lax pair of this equation, we obtain the corresponding infinite number of conservation laws and some properties of scattering data. By analyzing the direct scattering problem, we get a critical symmetric relation which is different from the local equations. A novel left-right Riemann-Hilbert problem is proposed to develop the inverse scattering theory. The potentials are recovered and the pure soliton solutions formula is obtained when the reflection coefficients are zero. Based on the zero types of scattering data, nine types of soliton solutions are obtained and three typical types are described in detail. In addition, some dynamic behaviors are given to illustrate the soliton characteristics of the space symmetric nonlocal Hirota equation.