Modified sine-Gordon theory with static multikinks

We construct a modified non-Bogomol’nyi-Prasad-Sommerfield sine-Gordon theory which supports stable static kinks of arbitrary topological degree <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>N</a:mi></a:math>. We use this toy model to study problems that are interesting for higher-dimensional soliton theories supporting multisolitons. We construct a 2-kink collective coordinate model and use it to generate scattering trajectories, which are compared to full-field dynamics. We find that the approximation works well, but starts to fail as radiation becomes more important, due to our model becoming less Bogomol’nyi-Prasad-Sommerfield or when the initial kink velocities are large. We also construct the quantum 2-kink using various approximations and consider how these quantum corrections affect the binding energy of the 2-kink. Published by the American Physical Society 2024