We exploit the gauge equivalence between the Hirota equation and the extended continuous Heisenberg equation to investigate how nonlocality properties of one system are inherited by the other. We provide closed generic expressions for nonlocal multi-soliton solutions for both systems. By demonstrating that a specific auto-gauge transformation for the extended continuous Heisenberg equation becomes equivalent to a Darboux transformation, we use the latter to construct the nonlocal multi-soliton solutions from which the corresponding nonlocal solutions to the Hirota equation can be computed directly. We discuss properties and solutions of a nonlocal version of the nonlocal extended Landau–Lifschitz equation obtained from the nonlocal extended continuous Heisenberg equation or directly from the nonlocal solutions of the Hirota equation.

中文翻译：

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非局部规范的对等：Hirota与扩展的连续Heisenberg和Landau–Lifschitz方程

我们利用Hirota方程和扩展的连续Heisenberg方程之间的规范等价关系来研究一个系统的非局部性质如何被另一个系统继承。我们为两个系统的非局部多孤子解决方案提供封闭的通用表达式。通过证明扩展的连续Heisenberg方程的特定自规变换等效于Darboux变换，我们使用后者构造了非局部多孤子解，从中可以直接计算Hirota方程的相应非局部解。我们讨论了从非局部扩展连续Heisenberg方程或直接从Hirota方程的非局部解获得的非局部扩展Landau–Lifschitz方程的非局部版本的性质和解。