Chaos in Partial Differential Equations available in Hardcover
- Pub. Date:
- International Press of Boston, Incorporated
This book presents a survey on existing results in the rapidly developing area of chaos in partial differential equations (PDEs). Nonlinear wave equations are the most important class of PDEs in natural sciences. Among these nonlinear wave equations, there is a class of equations called soliton equations that describe a wide spectrum of natural phenomena. The author and his collaborators have established a systematic theory on chaos in nonlinear wave equations. It is a standard program for proving the existence of chaos in perturbed soliton equations, using the following: (1) Darboux transformations for soliton equations, (2) isospectral theory for soliton equations under periodic boundary condition, (3) persistence of invariant manifolds and Fenichel fibers, (4) Melnikov analysis, (5) Smale horseshoes and symbolic dynamics, and (6) shadowing lemma and symbolic dynamics. This monograph is suitable for graduate students and researchers interested in differential equations, particularly in chaos in high dimensions.