  Starting from critical RSOS lattice models with appropriate inhomogeneities,
we derive two component nonlinear integral equations to describe the finite
volume ground state energy of the massive $\phi_{id,id,adj}$ perturbation of
the $SU(2)_k \times SU(2)_{k'} /SU(2)_{k+k'}$ coset models. When $k' \to
\infty$ while the value of $k$ is fixed, the equations correspond to the
current-current perturbation of the $SU(2)_k$ WZW model. Then modifying one of
the kernel functions of these equations, we propose two component nonlinear
integral equations for the fractional supersymmetric sine-Gordon models.
  The lattice versions of our equations describe the finite size effects in the
corresponding lattice models, namely in the critical RSOS($k,q$) models, in the
isotropic higher-spin vertex models, and in the anisotropic higher-spin vertex
models. Numerical and analytical checks are also performed to confirm the
correctness of our equations. These type of equations make it easier to treat
the excited state problem.
