Nonlinear Effects in Transmission Lines

Previous article Next article Nonlinear Effects in Transmission LinesE. CumberbatchE. Cumberbatchhttps://doi.org/10.1137/0115041PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] R. Landauer, Shock waves in nonlinear transmission lines and their effect on parametric amplification, IBM J. Res. Develop., 4 (1960), 391–401 MR0118314 CrossrefISIGoogle Scholar[2] R. B. Riley, An analysis of a nonlinear transmission line, Rep., 1707-1, Stanford Solid-State Electronics Laboratory, 1961 Google Scholar[3] B. A. Auld, , M. Di Domenico, Jr. and , R. H. Pantell, Travelling wave harmonic generation along nonlinear transmission lines, J. Appl. Phys., 33 (1962), 3537–3545 10.1063/1.1702443 CrossrefISIGoogle Scholar[4] A. Jeffrey, Wave propagation and electromagnetic shock wave formation in transmission lines, J. Math. Mech. 15 (1966), 1–13; corrigendum: ibid., 15 (1966), 346– MR0185994 0148.08106 Google Scholar[5] L. A. Ostrovskii, Formation and development of electromagnetic shock waves in transmission lines containing an unsaturated ferrite, Soviet Physics Tech. Phys., 8 (1964), 805–813 ISIGoogle Scholar[6] R. Courant and , K. O. Friedrichs, Supersonic Flow and Shock Waves, Interscience Publishers, Inc., New York, N. Y., 1948xvi+464 MR0029615 0041.11302 Google Scholar[7] E. Varley and , E. Cumberbatch, Relatively undistorted waves, to appear Google Scholar[8] E. Varley and , E. Cumberbatch, Nonlinear, high frequency sound waves, J. Inst. Mathematics and its Applications, 2 (1966), 133–143 CrossrefGoogle Scholar[9] Milton Van Dyke, Perturbation methods in fluid mechanics, Applied Mathematics and Mechanics, Vol. 8, Academic Press, New York, 1964x+229 MR0176702 0136.45001 Google Scholar[10] W. Chester, Resonant oscillations in closed tubes, J. Fluid Mech., 18 (1964), 44–64 0129.19504 CrossrefISIGoogle Scholar[11] David T. Blackstock, Connection between the Fay and Fubini solutions for plane sound waves of finite amplitude, J. Acoust. Soc. Amer., 39 (1966), 1019–1026 10.1121/1.1909986 MR0198801 0148.23204 CrossrefISIGoogle Scholar[12] David T. Blackstock, Propagation of plane sound waves of finite amplitude in nondissipative fluids, J. Acoust. Soc. Amer., 34 (1962), 9–30 10.1121/1.1909033 MR0152240 CrossrefISIGoogle Scholar[13] L. J. F. Broer, On the interaction of nonlinearity and dispersion in wave propagation, Appl. Sci. Res. Sec. B, 12 (1965), 113–129 10.1007/BF00382114 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Identification of Electric Transmission Line Deterioration by an Adaptive Observer2021 IEEE Conference on Control Technology and Applications (CCTA) | 9 Aug 2021 Cross Ref Large-Amplitude Shock Electromagnetic Wave in a Nonlinear Transmission Line Based on a Distributed Semiconductor DiodeSemiconductors, Vol. 53, No. 4 | 6 May 2019 Cross Ref Global existence of weak solutions to the nonlinear transmission line problemNonlinear Analysis: Theory, Methods & Applications, Vol. 17, No. 10 | 1 Jan 1991 Cross Ref Existence and asymptotic behavior of smooth solutions for the nonlinear transmission line problemApplicable Analysis, Vol. 39, No. 1 | 2 May 2007 Cross Ref Formation of shock discontinuities for a class of nonlinear transmission linesComputers & Mathematics with Applications, Vol. 15, No. 6-8 | 1 Jan 1988 Cross Ref A condition implying the global existence of C1 solutions for a class of nonlinear transmission linesComputers & Mathematics with Applications, Vol. 13, No. 9-11 | 1 Jan 1987 Cross Ref Small-Signal Second-Harmonic Generation by a Nonlinear Transmission Line (Comments)IEEE Transactions on Microwave Theory and Techniques, Vol. 35, No. 1 | 1 Jan 1987 Cross Ref ReferencesNonlinear Partial Differential Equations - Sequential and Weak Solutions | 1 Jan 1980 Cross Ref Effects of viscosity on long wavesJournal of Engineering Mathematics, Vol. 3, No. 1 | 1 Jan 1969 Cross Ref A simple electromagnetic shock wave analysis using boundaries in a moving frame of referenceIEEE Transactions on Magnetics, Vol. 3, No. 4 | 1 Dec 1967 Cross Ref Volume 15, Issue 2| 1967SIAM Journal on Applied Mathematics231-477 History Submitted:09 May 1966Accepted:18 November 1966Published online:13 July 2006 InformationCopyright © 1967 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0115041Article page range:pp. 450-463ISSN (print):0036-1399ISSN (online):1095-712XPublisher:Society for Industrial and Applied Mathematics