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Initial value problems and time‐periodic solutions for a nonlinear wave equation

1957; Wiley; Volume: 10; Issue: 3 Linguagem: Inglês

10.1002/cpa.3160100303

1097-0312

F. A. Ficken, B. A. Fleishman,

Nonlinear Waves and Solitons

Communications on Pure and Applied MathematicsVolume 10, Issue 3 p. 331-356 Article Initial value problems and time-periodic solutions for a nonlinear wave equation† F. A. Ficken, F. A. Ficken The University of Tennessee and Rensselaer Polytechnic InstituteSearch for more papers by this authorB. A. Fleishman, B. A. Fleishman The University of Tennessee and Rensselaer Polytechnic InstituteSearch for more papers by this author F. A. Ficken, F. A. Ficken The University of Tennessee and Rensselaer Polytechnic InstituteSearch for more papers by this authorB. A. Fleishman, B. A. Fleishman The University of Tennessee and Rensselaer Polytechnic InstituteSearch for more papers by this author First published: 1957 https://doi.org/10.1002/cpa.3160100303Citations: 24 † The results presented in this paper were obtained, in part, under Contracts N6ori-201T.0.1, Nonr-285(06) with the Office of Naval Research, while both authors were in residence at New York University. Further results were obtained under Contract NOrd 7386 between the U. S. Navy Bureau of Ordnance and the Applied Physics Laboratory, Johns Hopkins University, and Contract AF 18(600)-313 between the Office of Scientific Research of the Air Research and Development Command and the University of Tennessee. The final draft was prepared at the authors' present addresses. The authors acknowledge with thanks helpful suggestions by K. O. Friedrichs, E. Isaacson, P. D. Lax, P. Ungar, and J. J. Stoker; the latter originally suggested the time-periodic problem. AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinkedInRedditWechat Bibliography 1 Ficken, F. A., Periodic solutions of a nonlinear wave equation (Abstract), Bull. Amer. Math. Soc., Vol. 60, 1954, p. 148. 2 Ficken, F. A., Periodic solutions of a nonlinear wave equation (Abstract), Amer. Math. Monthly, Vol. 63, 1956, p. 529. 3 Fleishman, B. A., On the Periodic Solutions to an Initial-Value Problem for a Duffing-Type Nonlinear Wave Equation, Report No. 209, Bumblebee Series, Applied Physics Laboratory, The Johns Hopkins University, 1954. 4 Fleishman, B. A., Periodic solutions of a nonlinear wave equation (Abstract), Bull. Amer. Math. Soc., Vol. 59, 1953, p. 365. 5 Fleishman, B. A., Periodic solutions of a nonlinear wave equation (Abstract), Bull. Amer. Math. Soc., Vol. 61, 1955, p. 463. 6 Frank, P., and v. Mises, R., Differentialgleichungen der Physik, M. S. Rosenberg, New York, 1943. 7 Hyers, D. H., Linear topological spaces, Bull. Amer. Math. Soc., Vol. 51, 1945, pp. 1–21. 8 Stewart, F. M., Periodic solutions of a nonlinear wave equation (Abstract), Bull. Amer. Math. Soc., Vol. 60, 1954, p. 425. 9 Stoker, J. J., Oscillations périodiques des systèmes non linéaires ayant une infinité de degrés de liberté, Actes du Colloque International des Vibrations Non Linéaires, Pub. Sci. Tech. Ministère de 1'Air. No. 281, 1953. 10 Stoker, J. J., Nonlinear Vibrations, Interscience Publishers, New York, 1950. 11 Watson, G. N., A Treatise on the Theory of Bessel Functions, 2nd Ed., Cambridge University Press, 1944. Citing Literature Volume10, Issue31957Pages 331-356 ReferencesRelatedInformation