Integrable Semi-discrete Kundu-Eckhaus Equation: Darboux Transformation, Breather, Rogue Wave and Continuous Limit Theory
Integrable Semi-discrete Kundu-Eckhaus Equation: Darboux Transformation, Breather, Rogue Wave and Continuous Limit Theory
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可积半离散 Kundu-Eckhaus 方程：Darboux 变换、Breather、Rogue 波和连续极限理论
DOI：
10.1007/s00332-017-9399-9
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发表时间：
2018
影响因子：
3
通讯作者：
Zhu Zuo nong
中科院分区：
文献类型：
--
作者：
Zhao Hai qiong;Yuan Jinyun;Zhu Zuo nong
为了更深入地了解离散模型和连续对应模型之间的关系，从扩展的 Ablowitz-Ladik 层次结构的约简中导出了一个新的可积半离散 Kundu-Eckhaus 方程。通过证明Lax对和无限个守恒定律的存在性，证实了半离散模型的可积性。我们对半离散 Kundu-Eckhaus 方程详细分析了呼吸器的动态特性和有理解，揭示了连续方程中未发现的一些新的有趣现象。结果表明，包括Lax对、达布变换和显式解在内的离散系统理论在连续极限下系统地产生了它们的连续对应部分。
To get more insight into the relation between discrete model and continuous counterpart, a new integrable semi-discrete Kundu–Eckhaus equation is derived from the reduction in an extended Ablowitz–Ladik hierarchy. The integrability of the semi-discrete model is confirmed by showing the existence of Lax pair and infinite number of conservation laws. The dynamic characteristics of the breather and rational solutions have been analyzed in detail for our semi-discrete Kundu–Eckhaus equation to reveal some new interesting phenomena which was not found in continuous one. It is shown that the theory of the discrete system including Lax pair, Darboux transformation and explicit solutions systematically yields their continuous counterparts in the continuous limit.