Long-range interactions of kinks

Abstract

We present a computational analysis of the long-range interactions of solitary waves in higher-order field theories. Our vehicle of choice is the ${\phi }^8$ field theory, although we explore similar issues in example ${\phi }^{10}$ and ${\phi }^{12}$ models. In particular, we discuss the fundamental differences between the latter higher-order models and the standard ${\phi }^4$ model. Upon establishing the power-law asymptotics of the model's solutions' approach towards one of the steady states, we make the case that such asymptotics require particular care in setting up multi-soliton initial conditions. A naive implementation of additive or multiplicative ansätze gives rise to highly pronounced radiation effects and eventually leads to the illusion of a repulsive interaction between a kink and an antikink in such higher-order field theories. We propose and compare several methods for how to "distill" the initial data into suitable ansätze, and we show how these approaches capture the attractive nature of interactions between the topological solitons in the presence of power-law tails (long-range interactions). This development paves the way for a systematic examination of solitary wave interactions in higher-order field theories and raises some intriguing questions regarding potential experimental observations of such interactions. As an Appendix, we present an analysis of kink-antikink interactions in the example models via the method of collective coordinates.

arXiv comment41 pages, 18 figures, revtex4-1 class, v2: minor updates

References in corpus (45)

• Modeling the fifth dimension with scalars and gravity
• Oscillations and interactions of dark and dark-bright solitons in Bose-Einstein condensates
• Experimental observation of oscillating and interacting matter wave dark solitons
• Kink-antikink collisions in the phi^6 model
• Multiple atomic dark solitons in cigar-shaped Bose-Einstein condensates
• Kink interactions in the (1+1)-dimensional ${\phi }^6$ model
• Kink-kink and kink-antikink interactions with long-range tails
• Collective Coordinates in One-Dimensional Soliton Models Revisited
• Kink-antikink interactions in the double sine-Gordon equation and the problem of resonance frequencies
• Kink excitation spectra in the (1+1)-dimensional ${\phi }^8$ model
• Scattering of the ${\phi }^8$ kinks with power-law asymptotics
• Forces between Kinks and Antikinks with Long-range Tails
• Scattering of kinks of the sinh-deformed ${\phi }^4$ model
• Scattering of the double sine-Gordon kinks
• Successive phase transitions and kink solutions in ${\varphi }^8$, ${\varphi }^{10}$, and ${\varphi }^{12}$ field theories
• Resonant kink-antikink scattering through quasinormal modes
• Multi-kink collisions in the ${\varphi }^6$ model
• Kink-Antikink Scattering in ϕ^4 and ϕ^6 Models
• Dark energy, the electroweak vacua and collider phenomenology
• Solitary Wave Interactions In Dispersive Equations Using Manton's Approach
• Deformed defects for scalar fields with polynomial interactions
• Kink Dynamics in a Parametric ${\varphi }^6$ System: A Model With Controllably Many Internal Modes
• Giant gravitons: a collective coordinate approach
• Could the primordial radiation be responsible for vanishing of topological defects?
• Suppression of two-bounce windows in kink-antikink collisions
• Highly interactive kink solutions
• Analytical study of kinklike structures with polynomial tails
• Chiral asymmetry in propagation of soliton defects in crystalline backgrounds
• Perfectly invisible $\mathcal{P}\mathcal{T}$-symmetric zero-gap systems, conformal field theoretical kinks, and exotic nonlinear supersymmetry
• Topological defects with power-law tails
• Soliton defects in one-gap periodic system and exotic supersymmetry
• New scalar field models and their defect solutions
• A Mechanical Analog of the Two-bounce Resonance of Solitary Waves: Modeling and Experiment
• Scattering of kinks in a non-polynomial model
• Collective coordinate approximation to the scattering of solitons in the (1+1) dimensional NLS model
• Collective coordinate variable for soliton-potential system in sine-Gordon model
• Resonance phenomena in the ${\phi }^8$ kinks scattering
• From Supersymmetric Quantum Mechanics to Scalar Field Theories
• Construction of new scalar field models from the standard ${\varphi }^4$ theory
• From Scalar Field Theories to Supersymmetric Quantum Mechanics
• Excitation spectra of solitary waves in scalar field models with polynomial self-interaction
• Relativistic Collective Coordinate System of Solitons and Spinning Skyrmion
• Force between Kinks with Long-range Tails
• Collective coordinates of the Skyrme model coupled with fermions
• Gravity Waves Seeded by Turbulence and Magnetic Fields From a First Order Phase Transition With Non-Renormalizable Electroweak Vacua

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