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dc.contributor.authorTertychniy, Sergey ( Orcid Icon 0000-0002-6140-9665 )
dc.date.accessioned2021-08-17T17:55:23Z
dc.date.available2021-08-17T17:55:23Z
dc.date.issued2007-10-12
dc.identifier.citationTertychniy, S. I. (2007). General solution of overdamped Josephson junction equation in the case of phase-lock. Electronic Journal of Differential Equations, 2007(133), pp. 1-20.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/14347
dc.description.abstractThe first order nonlinear ordinary differential equation equation ϕ˙(t) + sin ϕ(t) = B + A cos ωt, which is commonly used as a simple model of an overdamped Josephson junction in superconductors is investigated. Its general solution is obtained in the case known as phase-lock where all but one solution converge to a common ‘essentially periodic’ attractor. The general solution is represented in explicit form in terms of the Floquet solution of a double confluent Heun equation. In turn, the latter solution is represented through the Laurent series which defines an analytic function on the Riemann sphere with punctured poles. The series coefficients are given in terms of infinite products of 2 × 2 matrices with a single zero element. The closed form of the phase-lock condition is obtained and represented as the condition for existence of a real root of a transcendental function. The efficient phase-lock criterion is conjectured, and its plausibility is confirmed in numerical tests.
dc.formatText
dc.format.extent20 pages
dc.format.medium1 file (.pdf)
dc.language.isoenen_US
dc.publisherTexas State University-San Marcos, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2007, San Marcos, Texas: Texas State University-San Marcos and University of North Texas.
dc.subjectOverdamped Josephson junctionen_US
dc.subjectNonlinear first order ODEen_US
dc.subjectLinear second order ODEen_US
dc.subjectDouble confluent Heun equationen_US
dc.subjectPhase locken_US
dc.subjectGeneral solutionen_US
dc.titleGeneral solution of overdamped Josephson junction equation in the case of phase-locken_US
dc.typepublishedVersion
txstate.documenttypeArticle
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.


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