Kink-kink and kink-antikink interactions with long-range tails

Abstract

In this Letter, we address the {long-range interaction} between kinks and antikinks, as well as kinks and kinks, in ${\phi }^{2n+4}$ field theories for $n>1$. The kink-antikink interaction is generically attractive, while the kink-kink interaction is generically repulsive. We find that the force of interaction decays with the $(\frac{2n}{n-1})$th power of their separation, and we identify the general prefactor for {\it arbitrary} $n$. Importantly, we test the resulting mathematical prediction with detailed numerical simulations of the dynamic field equation, and obtain good agreement between theory and numerics for the cases of $n=2$ (${\phi }^8$ model), $n=3$ (${\phi }^{10}$ model) and $n=4$ (${\phi }^{12}$ model).

6 pages, 3 figures, revtex4-1 class; v2 includes minor revisions; v3 corrects typos, accepted for publication in Physical Review Letters

References in corpus (21)

• Kink-antikink collisions in the phi^6 model
• Kink interactions in the (1+1)-dimensional ${\phi }^6$ model
• Collective Coordinates in One-Dimensional Soliton Models Revisited
• Long-range interactions of kinks
• Kink excitation spectra in the (1+1)-dimensional ${\phi }^8$ model
• Forces between Kinks and Antikinks with Long-range Tails
• Scattering of the ${\phi }^8$ kinks with power-law asymptotics
• Successive phase transitions and kink solutions in ${\varphi }^8$, ${\varphi }^{10}$, and ${\varphi }^{12}$ field theories
• Multi-kink collisions in the ${\varphi }^6$ model
• Deformed defects for scalar fields with polynomial interactions
• Kink Dynamics in a Parametric ${\varphi }^6$ System: A Model With Controllably Many Internal Modes
• Highly interactive kink solutions
• Creating kinks from particles
• Analytical study of kinklike structures with polynomial tails
• Family of Potentials with Power-Law Kink Tails
• Motion of domain walls and the dynamics of kinks in the magnetic Peierls potential
• A Clash of Kinks: Phase shifts in colliding non-integrable solitons
• A scattering theory of ultrarelativistic solitons
• New scalar field models and their defect solutions
• Kink Collisions in Curved Field Space
• From Supersymmetric Quantum Mechanics to Scalar Field Theories

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