Scattering of kinks in the $B{\phi }^4$ model

Abstract

In this study, based on the ${\phi }^4$ model, a new model (called the $B{\phi }^4$ 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 $B\le 1$. 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 $3.3<B\le 10$, 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.

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Cited by in corpus (1)

• (Anti-)Stokes Scattering on Kinks