I am trying to implement BJT non-linear equations in ADS, in that non-linear equation 3 voltage are depend on nodes of circuit (BJT used to design colpitts oscillator).

My question is how to use this node voltage to implement non-linear equations or there is other way that i can implement BJT Non-linear equations.

There are several ways to develop custom models in ADS. SDDs (Symbolically Defined Devices) are one approach; please check out the example workspace. A more advanced approach is to write user defined models using C code.