Kink solitons of the double-quadratic model in the presence of an external spatially inhomogeneous force

Dynamics of kink solitons of the double-quadratic model in the presence of an external, spatially inhomogeneous force F(x) is considered. Stability analysis of such solutions is performed. It is shown that similarly as for kinks of the phi⁴ equation there are differences between a stability condition for the kink treated as a point particle and the kink treated as a spatially extended object. These differences occur when the force F(x) possesses more than one zero and follow from interactions of kink wings (i.e., parts of kinks that are far from a kink center) with additional zeros of the force F(x).