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[null,"1.","Record Nr.",null,"UNINA9910151928003321"]
[null,null,"Autore",null,"Faou Erwan"]
[null,null,"Titolo",null,"Geometric Numerical Integration and Schrödinger Equations / / Erwan Faou"]
[null,null,"Pubbl/distr/stampa",null,"Zuerich, Switzerland, : European Mathematical Society Publishing House, 2012"]
[null,null,"ISBN",null,"3-03719-600-9"]
[null,null,"Descrizione fisica",null,"1 online resource (146 pages)"]
[null,null,"Collana",null,"Zurich Lectures in Advanced Mathematics (ZLAM)"]
[null,null,"Classificazione",null,"65-xx35-xx37-xx"]
[null,null,"Soggetti",null,"Numerical analysis"]
[{"$nulls":4},"Partial differential equations"]
[{"$nulls":4},"Dynamical systems and ergodic theory"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,null,"Sommario/riassunto","The goal of geometric numerical integration is the simulation of evolution  equations possessing geometric properties over long times. Of particular importance  are Hamiltonian partial differential equations typically arising in application  fields such as quantum mechanics or wave propagation phenomena. They  exhibit many important dynamical features such as energy preservation and  conservation of adiabatic invariants over long time. In this setting, a natural  question is how and to which extent the reproduction of such long time qualitative  behavior can be ensured by numerical schemes.  Starting from numerical examples, these notes provide a detailed analysis of the  Schrödinger equation in a simple setting (periodic boundary conditions, polynomial  nonlinearities) approximated by symplectic splitting methods. Analysis  of stability and instability phenomena induced by space and time discretization  are given, and rigorous mathematical explanations for them.  The book grew out of a graduate level course and is of interest to researchers  and students seeking an introduction to the subject matter."]