Asymptotic Solutions of Initial Value Problems for Nonlinear Partial Differential Equations

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Previous article Next article Asymptotic Solutions of Initial Value Problems for Nonlinear Partial Differential EquationsJoseph B. Keller and Stanley KogelmanJoseph B. Keller and Stanley Kogelmanhttps://doi.org/10.1137/0118067PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Julian D. Cole, Perturbation methods in applied mathematics, Blaisdell Publishing Co. Ginn and Co., Waltham, Mass.-Toronto, Ont.-London, 1968vi+260 MR0246537 0162.12602 Google Scholar[2] Edward A. Frieman, On a new method in the theory of irreversible processes, J. Mathematical Phys., 4 (1963), 410–418 10.1063/1.1703968 MR0160580 0124.45704 CrossrefISIGoogle Scholar[3] Joseph B. Keller and , Lu Ting, Periodic vibrations of systems governed by nonlinear partial differential equations, Comm. Pure Appl. Math., 19 (1966), 371–420 MR0205520 0284.35004 CrossrefISIGoogle Scholar[4] Martin H. Millman and , Joseph B. Keller, Perturbation theory of nonlinear boundary-value problems, J. Mathematical Phys., 10 (1969), 342–361 10.1063/1.1664849 MR0237867 0169.12702 CrossrefISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails On perturbation theory and its application in solving ordinary differential equations using the asymptotic expansion methodJournal of Physics: Conference Series, Vol. 1963, No. 1 | 1 Jul 2021 Cross Ref Causal properties of nonlinear gravitational waves in modified gravityPhysical Review D, Vol. 96, No. 6 | 21 September 2017 Cross Ref Introduction to Bifurcation and StabilityIntroduction to Perturbation Methods | 16 October 2012 Cross Ref Introduction to Asymptotic ApproximationsIntroduction to Perturbation Methods | 16 October 2012 Cross Ref The Method of HomogenizationIntroduction to Perturbation Methods | 16 October 2012 Cross Ref Matched Asymptotic ExpansionsIntroduction to Perturbation Methods | 16 October 2012 Cross Ref The WKB and Related MethodsIntroduction to Perturbation Methods | 16 October 2012 Cross Ref Multiple ScalesIntroduction to Perturbation Methods | 16 October 2012 Cross Ref Accuracy Improvement of the Method of Multiple Scales for Nonlinear Vibration Analyses of Continuous Systems with Quadratic and Cubic NonlinearitiesMathematical Problems in Engineering, Vol. 2010 | 1 Jan 2010 Cross Ref Asymptotic analysis of a perturbation problemJournal of Computational and Applied Mathematics, Vol. 190, No. 1-2 | 1 Jun 2006 Cross Ref ASYMPTOTIC APPROACH FOR NON-LINEAR PERIODICAL VIBRATIONS OF CONTINUOUS STRUCTURESJournal of Sound and Vibration, Vol. 249, No. 3 | 1 Jan 2002 Cross Ref Vibrational control of a non-linear elastic panelInternational Journal of Non-Linear Mechanics, Vol. 36, No. 4 | 1 Jun 2001 Cross Ref ON INTERACTIONS OF OSCILLATION MODES FOR A WEAKLY NON-LINEAR UNDAMPED ELASTIC BEAM WITH AN EXTERNAL FORCEJournal of Sound and Vibration, Vol. 235, No. 2 | 1 Aug 2000 Cross Ref An Asymptotic Theory for a Weakly Nonlinear Beam Equation with a Quadratic PerturbationG. 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