Using the Cauchy matrix approach, we derive a non-autonomous NijhoffQuispel-Capel(NQC) equation and its solutions. These solutions are formulated by a non-autonomous discrete dispersion relation and a generic Sylvester equation in which the coefficient matrix K can be an arbitrary constant square matrix. The non-autonomous NQC equation is shown to generate a non-autonomous Q3 equation in the non-autonomous Adler-Bobenko-Suris(ABS) list. We prove that the non-autonomous Q2, Q1, H3, H2, and H1 equations can b...
【基金】
supported by the National Natural Science Foundation of China(11371241);
the Scientific Research Foundation of the DPHE of China(20113108110002)
【更新日期】
2018-04-18
【分类号】
O175
【正文快照】
0 IntroductionThe Cauchy matrix approach was first proposed by Nijhoflf,et alJ1'2!as a system-atic method for constructing discrete integrable equations together with their solutionsas well as integrable structures.In this method,the discrete plain wave f
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