Focusing and defocusing Hirota equations with non-zero boundary conditions: Inverse scattering transforms and soliton solutions
Focusing and defocusing Hirota equations with non-zero boundary conditions: Inverse scattering transforms and soliton solutions
复制标题
具有非零边界条件的聚焦和散焦 Hirota 方程：逆散射变换和孤子解
DOI：
10.1016/j.cnsns.2019.104927
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发表时间：
2020
影响因子：
3.9
通讯作者：
Yan Zhenya
中科院分区：
文献类型：
--
作者：
Zhang Guoqiang;Chen Shuyan;Yan Zhenya
In this paper, we investigate the inverse scattering transforms and soliton solutions of both focusing and defocusing Hirota equations with non-zero boundary conditions (NZBCs). The inverse problems are solved via the study of the matrix Riemann-Hilbert problems. As a consequence, we present the general solutions for the potentials, and explicit expressions for the reflectionless potentials. Moreover, the trace formulae and theta conditions are also given. Particularly, we discuss the simple-pole and double-pole solutions for the focusing case, and the simple-pole solutions for the defocusing case. Moreover, the results of the focusing case with NZBCs can reduce to ones of the focusing case with zero-boundary condition (ZBC). These obtained solutions are useful to explain the related nonlinear wave phenomena. (c) 2019Elsevier B.V. All rights reserved.
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影响因子：
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DOI：
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