Travelling waves in a singularly perturbed sine-Gordon equation


Derks, Gianne and Doelman, Arjen and Gils, Stephan A. van and Visser, Timco (2003) Travelling waves in a singularly perturbed sine-Gordon equation. Physica D: Nonlinear phenomena, 180 (1-2). pp. 40-70. ISSN 0167-2789

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Abstract:We determine the linearised stability of travelling front solutions of a perturbed sine-Gordon equation. This equation models the long Josephson junction using the RCSJ model for currents across the junction and includes surface resistance for currents along the junction. The travelling waves correspond to the so-called fluxons and their linear stability is determined by calculating the Evans function. Surface resistance corresponds to a singular perturbation term in the governing equation, which specifically complicates the computation of the corresponding Evans function. Both the flow of quasi-particles across and along the junction stabilise the waves.
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Copyright:© 2003 Elsevier Science
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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