  Nonlinear z-independent solutions to a generalized Grad-Shafranov equation
(GSE) with up to quartic flux terms in the free functions and incompressible
plasma flow non parallel to the magnetic field are constructed
quasi-analytically. Through an ansatz the GSE is transformed to a set of three
ordinary differential equations and a constraint for three functions of the
coordinate x, in cartesian coordinates (x,y), which then are solved
numerically. Equilibrium configurations for certain values of the integration
constants are displayed. Examination of their characteristics in connection
with the impact of nonlinearity and sheared flow indicates that these
equilibria are consistent with the L-H transition phenomenology. For flows
parallel to the magnetic field one equilibrium corresponding to the H-state is
potentially stable in the sense that a sufficient condition for linear
stability is satisfied in an appreciable part of the plasma while another
solution corresponding to the L-state does not satisfy the condition. The
results indicate that the sheared flow in conjunction with the equilibrium
nonlinearity play a stabilizing role.
