We propose a new integrable coupled dispersionless equation with self-consistent sources (CDESCS). We obtain the Lax pair and the equivalent generalized Heisenberg ferromagnet equation (GHFE), demonstrating its integrability. Specifically, we explore the geometry of these equations. Last, we consider the relation between the motion of curves/surfaces and the CDESCS and the GHFE.

中文翻译：

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耦合无色散和广义海森堡铁磁方程与自洽源：几何和等价

我们提出了一个新的具有自洽源（CDESCS）的可积耦合无色散方程。我们获得了 Lax 对和等效的广义 Heisenberg 铁磁方程 (GHFE)，证明了它的可积性。具体来说，我们探索这些方程的几何形状。最后，我们考虑曲线/曲面的运动与 CDESCS 和 GHFE 之间的关系。