Scattering of kinks in the [formula omitted] model

Abstract

In this study, based on the φ4 model, a new model (called the Bφ4 model) is introduced in which the potential form for the values of the field whose magnitudes are greater than 1 is multiplied by the positive number B. All features related to a single kink (antikink) solution remain unchanged and are independent of parameter B. However, when a kink interacts with an antikink in a collision, the results will significantly depend on parameter B. Hence, for kink–antikink collisions, many features such as the critical speed, output velocities for a fixed initial speed, two-bounce escape windows, extreme values, and fractal structure in terms of parameter B are considered in detail numerically. The role of parameter B in the emergence of a nearly soliton behavior in kink–antikink collisions at some initial speed intervals is clearly confirmed. The fractal structure in the diagrams of escape windows is seen for the regime B≤1. However, for the regime B>1, this behavior gradually becomes fuzzing and chaotic as it approaches B=3.3. The case B=3.3 is obtained again as the minimum of the critical speed curve as a function of B. For the regime 3.3<B≤10, the chaotic behavior gradually decreases. However, a fractal structure is never observed. Nevertheless, it is shown that despite the fuzzing and shuffling of the escape windows, they follow the rules of the resonant energy exchange theory.