LEADER 03633nam 2200625 450 001 9910792702103321 005 20230809223755.0 010 $a3-11-038272-5 010 $a3-11-033568-9 024 7 $a10.1515/9783110335682 035 $a(CKB)3710000001177212 035 $a(MiAaPQ)EBC4843187 035 $a(DE-B1597)213692 035 $a(OCoLC)984625916 035 $a(OCoLC)985846032 035 $a(DE-B1597)9783110335682 035 $a(Au-PeEL)EBL4843187 035 $a(CaPaEBR)ebr11375508 035 $a(CaONFJC)MIL1006342 035 $a(OCoLC)983734730 035 $a(EXLCZ)993710000001177212 100 $a20170504h20172017 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $2rdacontent 182 $2rdamedia 183 $2rdacarrier 200 10$aNonlinear equations with small parameter$hVolume 1$iOscillations and resonances /$fSergey G. Glebov, Oleg M. Kiselev, Nikolai N. Tarkhanov 210 1$aBerlin, [Germany] ;$aBoston, [Massachusetts] :$cDe Gruyter,$d2017. 210 4$dİ2017 215 $a1 online resource (340 pages) 225 1 $aDe Gruyter Series in Nonlinear Analysis and Applications,$x0941-813X ;$vVolume 23/1 311 $a3-11-033554-9 320 $aIncludes bibliographical references and index. 327 $tFrontmatter -- $tPreface -- $tContents -- $tIntroduction -- $t1 Asymptotic expansions and series -- $t2 Asymptotic methods for solving nonlinear equations -- $t3 Perturbation of nonlinear oscillations -- $t4 Nonlinear oscillator in potential well -- $t5 Autoresonances in nonlinear systems -- $t6 Asymptotics for loss of stability -- $t7 Systems of coupled oscillators -- $tBibliography -- $tIndex 330 $aThis two-volume monograph presents new methods of construction of global asymptotics of solutions to nonlinear equations with small parameter. These allow one to match the asymptotics of various properties with each other in transition regions and to get unified formulas for the connection of characteristic parameters of approximate solutions. This approach underlies modern asymptotic methods and gives a deep insight into crucial nonlinear phenomena in the natural sciences. These include the outset of chaos in dynamical systems, incipient solitary and shock waves, oscillatory processes in crystals, engineering applications, and quantum systems. Apart from being of independent interest, such approximate solutions serve as a foolproof basis for testing numerical algorithms. This first volume presents asymptotic methods in oscillation and resonance problems described by ordinary differential equations, whereby the second volume will be devoted to applications of asymptotic methods in waves and boundary value problems. Contents Asymptotic expansions and series Asymptotic methods for solving nonlinear equations Nonlinear oscillator in potential well Autoresonances in nonlinear systems Asymptotics for loss of stability Systems of coupled oscillators 410 0$aDe Gruyter series in nonlinear analysis and applications ;$vVolume 23/1. 606 $aOscillations 610 $aNonlinear equations. 610 $aapproximate solutions. 610 $aglobal asymptotics. 610 $asmall parameter. 615 0$aOscillations. 676 $a531.32 686 $aSK 520$qSEPA$2rvk 700 $aGlebov$b Sergey G.$01516142 702 $aKiselev$b Oleg M. 702 $aTarkhanov$b Nikolai N. 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910792702103321 996 $aNonlinear equations with small parameter$93752389 997 $aUNINA