  Working on the framework of Relativistic Mean Field theory, we exposed the
effect of nonlinear isoscalar-isovector coupling on G2 parameter set on the
density dependence of nuclear symmetry energy in infinite nuclear matter. The
observables like symmetric energy and few related coefficients are studied
systematically. We presented the results of stiff symmetry energy at
sub-saturation densities and a soft variation at normal densities. Correlation
between the symmetric energy and the isoscalar-isovector coupling parameter
fully demonstrated for wide range of density. The work further extended to the
octet system and showed the effect of coupling over the equation of state.
