Carrier envelope phase dynamics of cavity solitons: soliton stability and scaling law

The relationship between carrier envelope phase (CEP) slip of cavity soliton (CS) and pump phase detuning is derived analytically and numerically. To preserve the stability of CS, CEP slip always equals to the pump phase detuning. When CEP slip fails to follow the pump phase detuning, CS becomes unstable. The locking between CEP slip and pump phase detuning results in a scaling law for CS.