PreprintCC BY 4.0arXiv
Evolution of instability fronts in sine-Gordon equation dynamics
Abstract
Solutions of the Whitham modulation equations for one-phase periodic waves obeying the sine-Gordon equation are found that describe the evolution of an oscillatory region behind an instability front propagating into the instability region. A simple self-similar solution describes the whole region between two fronts of instability resulting from a localized initial disturbance in the unstable state. Another hodograph solution represents typical waves close to the instability fronts. This theory generalizes the approach used previously for systems obeying the nonlinear Schroedinger equation.
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BibTeX
@misc{kamchatnov2026evolution,
title = {{Evolution of instability fronts in sine-Gordon equation dynamics}},
author = {A. M. Kamchatnov},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.04873},
eprint = {2609.04873},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.04873},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Evolution of instability fronts in sine-Gordon equation dynamics
AU - A. M. Kamchatnov
PY - 2026
DA - 2026/09/04
PB - arXiv
DO - 10.48550/arxiv.2609.04873
UR - https://arxiv.org/abs/2609.04873
AB - Solutions of the Whitham modulation equations for one-phase periodic waves obeying the sine-Gordon equation are found that describe the evolution of an oscillatory region behind an instability front propagating into the instability region. A simple self-similar solution describes the whole region between two fronts of instability resulting from a localized initial disturbance in the unstable state. Another hodograph solution represents typical waves close to the instability fronts. This theory generalizes the approach used previously for systems obeying the nonlinear Schroedinger equation.
ER -