Grébert, Benoît,
The Defocusing NLS Equation and Its Normal Form [electronic resource] / Benoît Grébert, Thomas Kappeler - Zuerich, Switzerland : European Mathematical Society Publishing House, 2014 - 1 online resource (175 pages) - EMS Series of Lectures in Mathematics (ELM) .
Restricted to subscribers: http://www.ems-ph.org/ebooks.php
The theme of this monograph is the nonlinear Schrödinger equation. This equation models slowly varying wave envelopes in dispersive media and arises in various physical systems such as water waves, plasma physics, solid state physics and nonlinear optics. More specifically, this book treats the defocusing nonlinear Schrödinger (dNLS) equation on the circle with a dynamical systems viewpoint. By developing the normal form theory it is shown that this equation is an integrable partial differential equation in the strongest possible sense. In particular, all solutions of the dNLS equation on the circle are periodic, quasi-periodic or almost-periodic in time and Hamiltonian perturbations of this equation can be studied near solutions far away from the equilibrium. The book is not only intended for specialists working at the intersection of integrable PDEs and dynamical systems, but also for researchers farther away from these fields as well as for graduate students. It is written in a modular fashion, each of its chapters and appendices can be read independently of each other.
9783037196311
10.4171/131 doi
Differential equations
Partial differential equations
Ordinary differential equations
Dynamical systems and ergodic theory
The Defocusing NLS Equation and Its Normal Form [electronic resource] / Benoît Grébert, Thomas Kappeler - Zuerich, Switzerland : European Mathematical Society Publishing House, 2014 - 1 online resource (175 pages) - EMS Series of Lectures in Mathematics (ELM) .
Restricted to subscribers: http://www.ems-ph.org/ebooks.php
The theme of this monograph is the nonlinear Schrödinger equation. This equation models slowly varying wave envelopes in dispersive media and arises in various physical systems such as water waves, plasma physics, solid state physics and nonlinear optics. More specifically, this book treats the defocusing nonlinear Schrödinger (dNLS) equation on the circle with a dynamical systems viewpoint. By developing the normal form theory it is shown that this equation is an integrable partial differential equation in the strongest possible sense. In particular, all solutions of the dNLS equation on the circle are periodic, quasi-periodic or almost-periodic in time and Hamiltonian perturbations of this equation can be studied near solutions far away from the equilibrium. The book is not only intended for specialists working at the intersection of integrable PDEs and dynamical systems, but also for researchers farther away from these fields as well as for graduate students. It is written in a modular fashion, each of its chapters and appendices can be read independently of each other.
9783037196311
10.4171/131 doi
Differential equations
Partial differential equations
Ordinary differential equations
Dynamical systems and ergodic theory