Family of Potentials with Power-Law Kink Tails

Abstract

We provide examples of a large class of one dimensional higher order field theories with kink solutions which asymptotically have a power-law tail either at one end or at both ends. We provide analytic solutions for the kinks in a few cases but mostly provide implicit solutions. We also provide examples of a family of potentials with two kinks, both of which have power law tails either at both ends or at one end. In addition, we show that for kinks with a power law tail at one end or both the ends, there is no gap between the zero mode and the continuum of the corresponding stability equation. This is in contrast to the kinks with exponential tail at both the ends in which case there is always a gap between the zero mode and the continuum.

40 pages, one table, no figures

References in corpus (5)

• Kink-kink and kink-antikink interactions with long-range tails
• Long-range interactions of kinks
• Forces between Kinks and Antikinks with Long-range Tails
• Highly interactive kink solutions
• Topological defects with power-law tails

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