New integrable coset sigma models

By using the general framework of affine Gaudin models, we construct a new class integrable sigma models. They are defined on coset direct product $N$ copies Lie group over some diagonal subgroup and they depend $3N-2$ free parameters. For $N=1$ corresponding model coincides with well-known symmetric space model. Starting from Hamiltonian formulation, derive Lagrangian for $N=2$ case show that it admits remarkably simple form in terms classical $\mathcal{R}$-matrix underlying integrability these We conjecture similar holds arbitrary $N$. Specifying our construction to $SU(2)$ $N=2$, eliminating one parameters, find three-parametric manifold $T^{1,1}$ as its target space. further comment connection results those existing literature.