Geometrically constrained sine-Gordon field: BPS solitons and their collisions

Abstract

We consider an enlarged $(1+1)$-dimensional model with two real scalar fields, $\varphi$ and $\chi$ whose scalar potential $V(\varphi ,\chi )$ has a standard ${\chi }^4$ sector and a sine-Gordon one for $\varphi$. These fields are coupled through a generalizing function $f(\chi )$ that appears in the scalar potential and controls the nontrivial dynamics of $\varphi$. We minimize the effective energy via the implementation of the BPS technique. We then obtain the Bogomol'nyi bound for the energy and the first-order equations whose solutions saturate that bound. We solve these equations for a nontrivial $f(\chi )$. As the result, BPS kinks with internal structures emerge. They exhibit a two-kink profile. i.e. an effect due to geometrical constrictions. We consider the linear stability of these new configurations. In this sense, we study the existence of internal modes that play an important role during the scattering process. We then investigate the kink-antikink collisions, and present the numerical results for the most interesting cases. We also comment about their most relevant features.

30 pages, 12 figures. Extended revised version published

References in corpus (42)

• Kink-antikink collisions in the phi^6 model
• Kink interactions in the (1+1)-dimensional ${\phi }^6$ model
• Kink-kink and kink-antikink interactions with long-range tails
• Magnetic domain walls in constrained geometries
• Kink-antikink interactions in the double sine-Gordon equation and the problem of resonance frequencies
• Spectral Walls in Soliton Collisions
• Scattering of kinks of the sinh-deformed ${\phi }^4$ model
• Scattering of the double sine-Gordon kinks
• Domain defects in systems of two real scalar fields
• Kink-Antikink Scattering in ϕ^4 and ϕ^6 Models
• Multi-kink collisions in the ${\varphi }^6$ model
• Kink-Antikink Collisions and Multi-Bounce Resonance Windows in Higher-Order Field Theories
• Reflection, transmutation, annihilation and resonance in two-component kink collisions
• Resonance structures in coupled two-component ${\varphi }^4$ model
• Suppression of two-bounce windows in kink-antikink collisions
• Geometrically Constrained Kinklike Configurations
• Manipulation of magnetic domain wall by ferroelectric switching: Dynamic magnetoelectricity at the nanoscale
• Non-topological kink scattering in a two-component scalar field theory model
• Extreme values of elastic strain and energy in sine-Gordon multi-kink collisions
• Spectral walls in multifield kink dynamics
• Boundary scattering in the ${\varphi }^6$ model
• Collisions of kinks in deformed ${\phi }^4$ and ${\phi }^6$ models
• Kink-antikink collisions in the ${\varphi }^8$ model: short-range to long-range journey
• Fermionic spectral walls in kink collisions
• Geometrically constrained kinklike configurations engendering long range, double exponential, half-compact and compact behavior
• Interaction Properties of the Periodic and Step-like Solutions of the Double-Sine-Gordon Equation
• Multi-sine-Gordon Models
• The collision of two-kinks defects
• Fermions in the presence of topological structures under geometric constrictions
• Collision of ${\varphi }^4$ kinks free of the Peierls-Nabarro barrier in the regime of strong discreteness
• Emerging Translational Variance: Vacuum Polarization Energy of the ${\varphi }^6$ kink
• Kink-antikink scattering in a quantum vacuum
• Mechanism to induce geometric constriction on kinks and domain walls
• A new look at the double sine-Gordon kink-antikink scattering
• Spectral walls in antikink-kink scattering in the ${\varphi }^6$ model
• Resonance structures in kink-antikink scattering in a quantum vacuum
• Kink scattering in the presence of geometric constrictions
• Geometrically constrained multifield models with BNRT solutions
• Kink Collision in the Noncanonical ${\phi }^6$ Model: A Model with Localized Inner Structures
• Kink Crystal
• Geometrically constrained localized configurations engendering non-topological profile
• Sine-Gordon kink lattice

Cited by in corpus (3)

• Exact BPS double-kinks in generalized ${\varphi }^4$, ${\varphi }^6$ and sine-Gordon models
• Some of the many uses of scalar fields: kinks, lumps, and geometric constraints
• Geometrically constrained multi-kink configurations in generalized impurity-doped field theories