  Guided wave modes in a symmetric slab waveguide formed by an isotropic
dielectric layer with cubic nonlinear response placed in the hyperbolic
surrounding medium are investigated theoretically. Optical axis of the
hyperbolic medium is normal to the slab plane. If dielectric permittivity of
the waveguide core is more than extraordinary permittivity of the hyperbolic
medium each TM mode has two cut-off frequencies. The dispersion relations for
these modes are found and numerically solved for cases of focusing and
defocussing medium of the core. Number of possible modes at given frequency
depends on the applied field intensity. It is shown that zero values of the TM
modes propagation constants are possible in the waveguide. Moreover in the
self-defocussing case they can be obtained by increasing field intensity. The
dependence of a propagation constant and width of the mode on radiation
intensity is obtained and analyzed.
