03633nam 2200625 450 991079270210332120230809223755.03-11-038272-53-11-033568-910.1515/9783110335682(CKB)3710000001177212(MiAaPQ)EBC4843187(DE-B1597)213692(OCoLC)984625916(OCoLC)985846032(DE-B1597)9783110335682(Au-PeEL)EBL4843187(CaPaEBR)ebr11375508(CaONFJC)MIL1006342(OCoLC)983734730(EXLCZ)99371000000117721220170504h20172017 uy 0engurcnu||||||||rdacontentrdamediardacarrierNonlinear equations with small parameterVolume 1Oscillations and resonances /Sergey G. Glebov, Oleg M. Kiselev, Nikolai N. TarkhanovBerlin, [Germany] ;Boston, [Massachusetts] :De Gruyter,2017.©20171 online resource (340 pages)De Gruyter Series in Nonlinear Analysis and Applications,0941-813X ;Volume 23/13-11-033554-9 Includes bibliographical references and index.Frontmatter -- Preface -- Contents -- Introduction -- 1 Asymptotic expansions and series -- 2 Asymptotic methods for solving nonlinear equations -- 3 Perturbation of nonlinear oscillations -- 4 Nonlinear oscillator in potential well -- 5 Autoresonances in nonlinear systems -- 6 Asymptotics for loss of stability -- 7 Systems of coupled oscillators -- Bibliography -- IndexThis two-volume monograph presents new methods of construction of global asymptotics of solutions to nonlinear equations with small parameter. These allow one to match the asymptotics of various properties with each other in transition regions and to get unified formulas for the connection of characteristic parameters of approximate solutions. This approach underlies modern asymptotic methods and gives a deep insight into crucial nonlinear phenomena in the natural sciences. These include the outset of chaos in dynamical systems, incipient solitary and shock waves, oscillatory processes in crystals, engineering applications, and quantum systems. Apart from being of independent interest, such approximate solutions serve as a foolproof basis for testing numerical algorithms. This first volume presents asymptotic methods in oscillation and resonance problems described by ordinary differential equations, whereby the second volume will be devoted to applications of asymptotic methods in waves and boundary value problems. Contents Asymptotic expansions and series Asymptotic methods for solving nonlinear equations Nonlinear oscillator in potential well Autoresonances in nonlinear systems Asymptotics for loss of stability Systems of coupled oscillators De Gruyter series in nonlinear analysis and applications ;Volume 23/1.OscillationsNonlinear equations.approximate solutions.global asymptotics.small parameter.Oscillations.531.32SK 520SEPArvkGlebov Sergey G.1516142Kiselev Oleg M.Tarkhanov Nikolai N.MiAaPQMiAaPQMiAaPQBOOK9910792702103321Nonlinear equations with small parameter3752389UNINA