The Sine-Gordon Wobble
German Ka"lbermann
TL;DR
This paper introduces and studies numerically a new class of nonperturbative, oscillatory solutions called wobble solitons in the Sine-Gordon equation, showing perturbed kinks decay into these wobble states.
Contribution
It presents the first numerical construction and analysis of wobble solitons as nonperturbative solutions of the Sine-Gordon equation, expanding understanding of its solution space.
Findings
Wobble solitons are nonperturbative, oscillatory solutions with winding number one.
Perturbed kinks decay into wobble solitons.
Wobble solitons are numerically constructed and characterized.
Abstract
Nonperturbative, oscillatory, winding number one solutions of the Sine-Gordon equation are presented and studied numerically. We call these nonperturbative shape modes {\sl wobble} solitons. Perturbed Sine-Gordon kinks are found to decay to {\sl wobble} solitons.
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Taxonomy
TopicsNonlinear Photonic Systems · Nonlinear Waves and Solitons · Quantum Mechanics and Non-Hermitian Physics