We review recent works on modeling of dynamics of kinks in 1+1 dimensional $\phi^4$ theory and other related models, like sine-Gordon model or $\phi^6$ theory. We discuss how the spectral structure of small perturbations can affect the dynamics of non-perturbative states, such as kinks or oscillons. We describe different mechanisms, which may lead to the occurrence of the resonant structure in the kink-antikink collisions. We explain the origin of the radiation pressure mechanism, in particular, the appearance of the negative radiation pressure in the $\phi^4$ and $\phi^6$ models. We also show that the process of production of the kink-antikink pairs, induced by radiation is chaotic.
CITATION STYLE
Romańczukiewicz, T., & Shnir, Y. (2019). Some Recent Developments on Kink Collisions and Related Topics (pp. 23–49). https://doi.org/10.1007/978-3-030-11839-6_2
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