Rational solutions to Q3(delta) in the Adler-Bobenko-Suris list and degenerations
Rational solutions to Q3(delta) in the Adler-Bobenko-Suris list and degenerations
复制标题
Adler-Bobenko-Suris 列表中 Q3(delta) 的有理解和退化
DOI：
10.1080/14029251.2019.1544793
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发表时间：
2019
影响因子：
0.7
通讯作者：
Da-jun Zhang
中科院分区：
文献类型：
--
作者：
Song-lin Zhao;Da-jun Zhang
利用晶格势Korteweg-de弗里斯（lpKdV）方程以及lpKdV与晶格势修正KdV（lpmKdV）之间的两个Miura变换和NQC方程，导出了Nijhoff-Quispel-卡佩尔（NQC）方程的Casoratian形式的有理解.这使我们能够提出合理的解决方案，为整个阿德勒-博本科-苏里斯（ABS）的名单，除了Q4。利用NQC方程与Q3δ之间孤子解的Miura变换和ABS表中Q3δ到Q2、Q1δ、H3δ、H2和H1的孤子简并。我们证明了三浦变换和简并对于通常被认为是孤子长波极限的有理解也是有效的。所有的有理解都可以用{zj}表示，{zj}是（n，m）的线性函数。
We derive rational solutions in Casoratian form for the Nijhoff-Quispel-Capel (NQC) equation by using the lattice potential Korteweg-de Vries (lpKdV) equation and two Miura transformations between the lpKdV and the lattice potential modified KdV (lpmKdV) and the NQC equation. This allows us to present rational solutions for the whole Adler-Bobenko-Suris (ABS) list except Q4. The known Miura transformation for soliton solutions between the NQC equation and Q3δand the known degenerations for solitons from Q3δto Q2, Q1δ, H3δ, H2 and H1 in the ABS list are used. We show that the Miura transformation and degenerations are valid as well for rational solutions which are usually considered as “long-wave-limit” of solitons. All the rational solutions can be expressed in terms of {zj} which are linear functions of (n,m).