摘要：In this paper, we consider a weakly coupled sinh-Gordon equation which takes values in a commutative Frobenius subalgebra of g l ( 2 , C ) $gl(2,\mathbb {C})$ . Then we construct some nonlocal symmetries of the Frobenius sinh-Gordon system using its Bäcklund transformation and infinitesimal transformations. Based on the nonlocal symmetries, we show some conserved densities of the Frobenius sinh-Gordon system. Using these symmetries, we also construct some new coupled integro-differential systems.
