Deformation of sine-Gordon two-soliton solutions in φ4 kink-antikink configurations
Abstract
In this work, we construct analytical kink-antikink (KK̅) configurations in the non-integrable φ4 model by mapping exact solutions of the integrable sine-Gordon system via a field deformation. This procedure yields two distinct classes of configurations, parametrized by the initial half-separation and velocity. We compare these profiles with the standard additive superposition Ansatz in terms of vacuum structure and equation-of-motion residuals, deriving explicit closed-form expressions for the corresponding integrated squared residuals. For small separations, the mapped soliton-antisoliton configurations exhibit appreciably smaller residuals than the naive superposition Ansatz, which in turn performs better than the mapped two-soliton configurations. Although the mapped fields are not exact solutions of the φ4 equation of motion, they provide mathematically consistent, topologically sound, and physically motivated initial data for numerical studies of kink-antikink scattering and resonance phenomena.
Related
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BibTeX
@misc{marjaneh2026deformation,
title = {{Deformation of sine-Gordon two-soliton solutions in $φ^4$ kink-antikink configurations}},
author = {Aliakbar Moradi Marjaneh and Danial Saadatmand and Fabiano C. Simas and Jarah Evslin and Dionisio Bazeia},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.15091},
eprint = {2609.15091},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.15091},
}
RIS
TY - UNPB
TI - Deformation of sine-Gordon two-soliton solutions in φ^4 kink-antikink configurations
AU - Aliakbar Moradi Marjaneh
AU - Danial Saadatmand
AU - Fabiano C. Simas
AU - Jarah Evslin
AU - Dionisio Bazeia
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.15091
UR - https://arxiv.org/abs/2609.15091
AB - In this work, we construct analytical kink-antikink (KK̅) configurations in the non-integrable φ^4 model by mapping exact solutions of the integrable sine-Gordon system via a field deformation. This procedure yields two distinct classes of configurations, parametrized by the initial half-separation and velocity. We compare these profiles with the standard additive superposition Ansatz in terms of vacuum structure and equation-of-motion residuals, deriving explicit closed-form expressions for the corresponding integrated squared residuals. For small separations, the mapped soliton-antisoliton configurations exhibit appreciably smaller residuals than the naive superposition Ansatz, which in turn performs better than the mapped two-soliton configurations. Although the mapped fields are not exact solutions of the φ^4 equation of motion, they provide mathematically consistent, topologically sound, and physically motivated initial data for numerical studies of kink-antikink scattering and resonance phenomena.
ER -