Riemann-Hilbert approach for the integrable discrete Hirota equation with bounded boundary conditions in the presence of a discrete spectrum

被引：0

作者：

Liu, Ya-Hui ^{[1
]}

Guo, Rui ^{[1
]}

Zhang, Jian-Wen ^{[1
]}

机构：

[1] Taiyuan Univ Technol, Sch Math, Taiyuan 030024, Peoples R China

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2025年 / 48卷 / 02期

关键词：

nonzero boundary conditions; Riemann-Hilbert approach; soliton solutions; the integrable discrete Hirota equation; NONLINEAR SCHRODINGER-EQUATION; INVERSE SCATTERING TRANSFORM; DARBOUX TRANSFORMATION; SOLITON-SOLUTIONS; SYSTEM;

D O I：

10.1002/mma.10400

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, the Riemann-Hilbert (RH) approach for the integrable discrete Hirota equation with bounded boundary conditions is presented. In the direct scattering problem, we study the analyticity, asymptotics, symmetries of the eigenfunctions, and scattering coefficients and analyze the distribution of discrete eigenvalues. In the inverse scattering problem, the RH problem is constructed and solved as well as the reconstruction formula of potential is derived based on asymptotics. Finally, combining the time evolution, we solve the first- and second-order dark soliton solutions on the nonzero background under the reflectionless condition.

引用

页码：1636 / 1658

页数：23

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