5983

5598

كارشناسي ارشد

دستگاه هاي ديناميكي

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1389

[نه]،157ص.: مصور،جدول،نمودار

ص.ع.به فارسي و انگليسي

حميدرضا ظهوري زنگنه

رسول عاشقي

10/3/90

مجيد گازر، رضا مزروعي

رياضي

ID5598

به فارسي و انگليسي: قابل رويت در نسخه ديجيتالي

Bifurcations of travelling wave solutions for four classes of nonlinear wave equations Masoud Mosaddeghi m mosaddeghi@math iut ac ir 6 December 2010 Master of Science Thesis Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Hamid Reza Z Zangeneh hamidz@cc iut ac ir Advisor Dr Rasoul Asheghi r asheghi@cc iut ac ir 2000 MSC 35Q53 Key words travelling wave solutions Bifurcation theory Abstract In this thesis Four large classes of nonlinear wave equations are studied and the existence of solitary wave kink and anti kink wave and uncountably many periodic wave solutions is proved The analysis is based on the bifurcation theory of dynamical systems Under some parametric conditions various su cient conditions for the existence of the aforementioned wave solutions are derived Moreover all possible exact parametric representations of solitary wave kink and anti kink wave and periodic wave solutions are obtained and classi ed One of these equations to be numerically simulated Another these equations is Kuramoto Sivashinsky equation The Kuramoto Sivashinsky equation is an important model equation in studies of nonlinear partial di erential equations PDEs This thesis is not about the Kuramoto Sivashinsky PDE as such but about the nonlinear ordinary di erential equation ODE with one parameter c which describes the travelling wave solutions yxxx c y yx The study of nonlinear ODEs is hard This Equation has a symmetry S which is very signi cant for the bifurcation behaviour and the numerical path following program AUTO is used to explore some of this complexity We invatigate the consequences of putting together a period doubling and saddle node bifurcation to form a closed loop the noose bifurcation where the two branches of the period doubling evolve so as to come together again and annihilate in a saddle node The noose is non trivial because of the topological properties of periodic orbits in phase space interlinking between orbits and self linking twisting of the manifolds of orbits We ask whether the noose is generic typical of all ordinary di erential equations or daes it require special properties In explaining the noose we introduce some useful ideas from the analytical literature on ODEs generic properties and bifurcations and some simple applications of knot theory The noose is a good place from which to hang these ideas

حميدرضا ظهوري زنگنه

رسول عاشقي

مجيد گازر، رضا مزروعي