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arXiv · 2603.18605

Radiation damping of the soliton internal mode in 1D quadratic Klein-Gordon equation

Piotr Bizoń·Tomasz Romańczukiewicz
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Abstract

We study long-time dynamics of small even perturbations of the soliton in 1D quadratic Klein-Gordon equation. The soliton possesses both an internal mode and the unstable mode. On a codimension-one manifold of fine-tuned initial data the instability is suppressed and the internal mode decays slowly by transferring energy into the continuum. We show that this decay and the associated nonlinear frequency shift are accurately captured by a cubic resonant approximation, with the damping rate determined by a Fermi golde rule-type coefficient. This provides a quantitative description of irreversible energy transfer from the internal mode to dispersive radiation.

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Piotr Bizoń, Tomasz Romańczukiewicz. 2026-03-19. Radiation damping of the soliton internal mode in 1D quadratic Klein-Gordon equation. https://arxiv.org/abs/2603.18605

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