Analytical short- and long-range kink-like structures in scalar field models with polynomial interactions
arXiv:2409.01961 · doi:10.1016/j.aop.2024.169915
Abstract
We investigate a class of scalar field models which engender kink-like solutions in the presence of polynomial potentials that allows for modifications of the tails of the localized configurations. We introduce a parameter in the potential that controls the classical mass associated to its minima. By using the first-order framework developed by Bogomol'nyi, we obtain analytical solutions that become more and more interactive as we increase such parameter. By investigating the limit in which the parameter tends to infinite, the kink solution gets power law tails, and we show that this feature is related to the behavior of the classical mass, which vanishes in the aforementioned limit. We also investigate the stability against small fluctuations, with the results unveiling that, depending on the values of the parameter, the stability potential may support several bound states and also, it may attain a volcano-like profile.
8 pages, 7 figures; text improved and references added
References in corpus (28)
- An Alternative to Compactification
- Modeling the fifth dimension with scalars and gravity
- Localized nonlinear waves in systems with time- and space-modulated nonlinearities
- Generalized Global Defect Solutions
- Solitons with Cubic and Quintic Nonlinearities Modulated in Space and Time
- Kink-kink and kink-antikink interactions with long-range tails
- Magnetic domain walls in constrained geometries
- Long-range interactions of kinks
- Kink excitation spectra in the (1+1)-dimensional model
- Forces between Kinks and Antikinks with Long-range Tails
- From Kinks to Compactons
- Kink-Antikink Collisions and Multi-Bounce Resonance Windows in Higher-Order Field Theories
- Suppression of two-bounce windows in kink-antikink collisions
- Highly interactive kink solutions
- Analytical study of kinklike structures with polynomial tails
- Interaction between kinks and antikinks with double long-range tails
- Explicit kinks in higher-order field theories
- Kink-antikink collisions in the model: short-range to long-range journey
- Kinks in higher-order polynomial models
- Geometrically constrained kinklike configurations engendering long range, double exponential, half-compact and compact behavior
- Compact Structures in Standard Field Theory
- Forces Between Kinks in Theory
- Defect structures in sine-Gordon-like models
- Scattering of compactlike structures
- Collisions between kinks with long-range tails: a simple and efficient method
- A soliton with a long-range tail
- Highly-enhanced propagation of long-range kinks in heterogeneous media
- Scattering of kinks in scalar-field models with higher-order self-interactions