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arXiv · 1712.08473

Solitons in the Presence of a Small, Slowly Varying Electric Field

Timur Mashkin
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Abstract

We consider the perturbed sine-Gordon equation $\theta_{tt}-\theta_{xx}+\sin \theta= \varepsilon^2 f(\varepsilon x)$, where the external perturbation $\varepsilon^2 f(\varepsilon x)$ corresponds to a small, slowly varying electric field. We show that the initial value problem with an appropriate initial state close enough to the solitary manifold has a unique solution, which follows up to time $1/{\varepsilon}$ and errors of order $\varepsilon^{ 3/4}$ a trajectory on the solitary manifold. The trajectory on the solitary manifold is described by ODEs, which agree approximately up to errors of order $\varepsilon^3$ with Hamilton equations for the restricted to the solitary manifold sine-Gordon Hamiltonian.

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Timur Mashkin. 2017-12-21. Solitons in the Presence of a Small, Slowly Varying Electric Field. https://arxiv.org/abs/1712.08473

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