Description
Book SynopsisAn introductory textbook about nonlinear dynamics of PDEs, with a focus on problems over unbounded domains and modulation equations. The presentation is example-oriented, and new mathematical tools are developed step by step, giving insight into some important classes of nonlinear PDEs and nonlinear dynamics phenomena which may occur in PDEs.
Trade ReviewThis book as a whole is more than the sum of its chapters and deserves being slowly and thoughtfully read from the beginning to the end." — Michael Zaks,
Mathematical Reviews"This is an excellent text which can be used for several graduate courses in mathematics departments." — Dmitry Pelinovsky,
Zentralblatt MATH"The combination of rigor with simultaneous attention to associated real physical systems makes it particularly appealing." — William Satzer,
MAA ReviewsTable of Contents
- Basic ODE dynamics
- Dissipative dynamics
- Hamiltonian dynamics
- PDEs on an interval
- The Navier-Stokes equations
- Some dissipative PDE models
- Three canonical modular equations
- Reaction-diffusion systems
- Dynamics of pattern and the GL equation
- Wave packets and the NLS equation
- Long waves and their modular equations
- Center manifold reduction and spatial dynamics
- Diffusive stability
- Bibliography
- Index
- List of symbols.
