By embedding a free function into discrete zero curvature equation, we generalize the original hierarchy of integrable differential-difference equations into a new hierarchy which includes the famous relativistic Toda hierarchy. Infinitely many conservation laws and Darboux transformation for the first nontrivial system in the new hierarchy are constructed with the help of its Lax pair. The exact solutions of the system are generated by applying the obtained Darboux transformation. Finally, the figures of one- and two-soliton solutions with proper parameters are presented to illustrate the structures of soliton solutions.

中文翻译：

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可积微分方程和 Darboux 变换的层次结构

通过将自由函数嵌入离散零曲率方程，我们将可积微分方程的原始层次推广到一个新的层次，其中包括著名的相对论 Toda 层次。新层次结构中第一个非平凡系统的无穷多个守恒定律和 Darboux 变换是在其 Lax 对的帮助下构建的。系统的精确解是通过应用获得的 Darboux 变换生成的。最后，给出了具有适当参数的一和二孤子解的图形来说明孤子解的结构。