Travelling waves in a singularly perturbed sine-Gordon equations

G.L.A. Derks, Gianne Derks, Arjen Doelman, Stephanus A. van Gils, T.P.P. Visser

Research output: Contribution to journalArticleAcademicpeer-review

15 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)40-70
JournalPhysica D
Volume180
Issue number1-2
DOIs
Publication statusPublished - 2003

Fingerprint

sine-Gordon equation
Evans Function
Surface resistance
Sine-Gordon Equation
Singularly Perturbed
traveling waves
Traveling Wave
Travelling Fronts
Josephson Junction
Quasiparticles
Linear Stability
Singular Perturbation
Governing equation
elementary excitations
Josephson junctions
Term
Model
perturbation
Resistance

Keywords

  • METIS-211866
  • Evans function
  • IR-74894
  • Perturbed sine-Gordon equation
  • Travelling waves

Cite this

Derks, G.L.A. ; Derks, Gianne ; Doelman, Arjen ; van Gils, Stephanus A. ; Visser, T.P.P. / Travelling waves in a singularly perturbed sine-Gordon equations. In: Physica D. 2003 ; Vol. 180, No. 1-2. pp. 40-70.
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Derks, GLA, Derks, G, Doelman, A, van Gils, SA & Visser, TPP 2003, 'Travelling waves in a singularly perturbed sine-Gordon equations' Physica D, vol. 180, no. 1-2, pp. 40-70. https://doi.org/10.1016/S0167-2789(03)00050-2

Travelling waves in a singularly perturbed sine-Gordon equations. / Derks, G.L.A.; Derks, Gianne; Doelman, Arjen; van Gils, Stephanus A.; Visser, T.P.P.

In: Physica D, Vol. 180, No. 1-2, 2003, p. 40-70.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Travelling waves in a singularly perturbed sine-Gordon equations

AU - Derks, G.L.A.

AU - Derks, Gianne

AU - Doelman, Arjen

AU - van Gils, Stephanus A.

AU - Visser, T.P.P.

PY - 2003

Y1 - 2003

N2 - 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.

AB - 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.

KW - METIS-211866

KW - Evans function

KW - IR-74894

KW - Perturbed sine-Gordon equation

KW - Travelling waves

U2 - 10.1016/S0167-2789(03)00050-2

DO - 10.1016/S0167-2789(03)00050-2

M3 - Article

VL - 180

SP - 40

EP - 70

JO - Physica D

JF - Physica D

SN - 0167-2789

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