Behavior of φ⁴ kinks in the presence of external forces

The influence of external forces on the properties of kinks in the φ⁴ equation is investigated. Depending on characteristic parameters, the model describes the interaction of a kink with a material impurity or a phase boundary. In the presence of external forces, there are differences between stability conditions for a kink treated as a point particle and for a kink investigated as an extended object. These differences come from interactions of kink wings with zeros of external forces. An inhomogeneous external force changes the spectrum of small oscillations around a kink, and additional bound states can appear. When this force has the form of a static two-well potential, chaotic kink motion is possible, provided the amplitude of an additional ac force is higher than a critical value.