We examine the question of the integrability of the recently defined ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$-graded sine-Gordon model, which is a natural generalisation of the supersymmetric sine-Gordon equation. We do this via appropriate auto-Bäcklund transformations, construction of conserved spinor-valued currents and a pair of infinite sets of conservation laws.

中文翻译：

---

Z2×Z2 分级的正弦-戈登方程是否可积？

我们检查最近定义的可积性问题 ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$-graded sine-Gordon 模型，它是超对称正弦-戈登方程的自然推广。我们通过适当的 auto-Bäcklund 变换、构造守恒的自旋值电流和一对无限的守恒定律来做到这一点。