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Nonlinear Perturbations
dc.contributor.authorCoffey, Timothy Patrick.en_US
dc.contributor.authorFord, G. W.en_US
dc.date.accessioned2010-05-06T20:57:17Z
dc.date.available2010-05-06T20:57:17Z
dc.date.issued1969-06en_US
dc.identifier.citationCoffey, Timothy P.; Ford, G. W. (1969). "Nonlinear Perturbations." Journal of Mathematical Physics 10(6): 998-1003. <http://hdl.handle.net/2027.42/69667>en_US
dc.identifier.urihttps://hdl.handle.net/2027.42/69667
dc.description.abstractThe perturbation theory of Bogoliubov and Mitropolsky for systems having a single rapid phase is generalized to systems having several rapid phases. It is shown that one can avoid the classic problem of small divisors to all orders in the perturbation theory. The method has the advantage of providing a single approach to many problems conventionally treated by a variety of specialized techniques.en_US
dc.format.extent3102 bytes
dc.format.extent369162 bytes
dc.format.mimetypetext/plain
dc.format.mimetypeapplication/pdf
dc.publisherThe American Institute of Physicsen_US
dc.rights© The American Institute of Physicsen_US
dc.titleNonlinear Perturbationsen_US
dc.typeArticleen_US
dc.subject.hlbsecondlevelPhysicsen_US
dc.subject.hlbtoplevelScienceen_US
dc.description.peerreviewedPeer Revieweden_US
dc.contributor.affiliationumDepartment of Physics, The University of Michigan, Ann Arbor, Michiganen_US
dc.description.bitstreamurlhttp://deepblue.lib.umich.edu/bitstream/2027.42/69667/2/JMAPAQ-10-6-998-1.pdf
dc.identifier.doi10.1063/1.1664946en_US
dc.identifier.sourceJournal of Mathematical Physicsen_US
dc.identifier.citedreferenceN. N. Krylov and N. N. Bogoliubov, Introduction to Non‐Linear Mechanics (Academy of Sciences of the Ukranian S.S.R., Kiev, 1937), trans, by S. Lefschetz in Annals of Mathematics Studies, No. 11 (Princeton University Press, Princeton, N.J., 1947).en_US
dc.identifier.citedreferenceK. M. Case, Suppl. Progr. Theoret. Phys. (Kyoto) 37, 1 (1966). See also R. Y. Y. Lee, “On a New Perturbation Method” Thesis, The University of Michigan, Ann Arbor, 1964.en_US
dc.identifier.citedreferenceN. N. Bogoliubov and D. N. Zubarev, Ukrain. Mat. Zh. 7, 5 (1955); N. N. Bogoliubov and Y. A. Mitropolsky, Asymptotic Methods in the Theory of Non‐Linear Oscillations (Hindustan Publishing Co., Delhi, India, 1961), Chaps. 5 and 6. See also N. Minorsky, Nonlinear Oscillations (D. van Nostrand Co., Princeton, N.J., 1962), and M. Kruskal, J. Math. Phys. 3, 806 (1962).en_US
dc.identifier.citedreferenceT. P. Coffey, J. Math. Phys. 10, 1362 (1969).en_US
dc.identifier.citedreferenceThe generalization to the general case where the right‐hand sides of (2.1) are power series in ϵ is straightforward.en_US
dc.identifier.citedreferenceR. A. Struble and J. E. Fletcher, J. Math. Phys. 2, 880 (1961). See also N. Minorsky, Ref. 2, pp. 219–224 and pp. 329–338.en_US
dc.identifier.citedreferenceFor a proof see T. P. Coffey, “Analytical Methods in the Theory of Non‐Linear Oscillations,” thesis, The University of Michigan, Ann Arbor, 1966.en_US
dc.identifier.citedreferenceFor a proof, see Ref. 7.en_US
dc.owningcollnamePhysics, Department of


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