Spatial Patterns

"The book is on the one hand written for mathematicians and mathematical physicists, who want to learn about this fascinating subject, and on the other hand also accessible to graduate students. One finds a large amount of exercises and open problems that can serve as a starting point for further research ... The authors have produced a well-written book, which gives a good picture of what is known about the canonical equation." -Quantum Information and Computation "The book is very well written in a very clear and readable style, which makes it accessible to a nonspecialist or graduate student. There are a large number of exercises, which fill in details of proofs or provide illuminating examples or straightforward generalisations as well as a good number of open problems. There are also a large number of numerically computed graphs of branching curves and bifurcation curves throughout the book, which provide insights into the mathematically formulated results. The book is a valuable contribution to the literature, for both the specialist and the nonspecialist reader." -Mathematical Reviews

• 1 Introduction.- 1.1 Model equations.- 1.2 The Fisher–Kolmogorov equation.- 1.3 An overview.- 1.4 Methods.- 1.5 About the presentation.- 1.6 Bibliographical notes.- I The Symmetric Bistable Equation.- 2 Real Eigenvalues.- 3 Estimates.- 4 Periodic Solutions.- 5 Kinks and Pulses.- 6 Chaotic Solutions.- 7 Variational Problems.- II Related Equations.- 8 The Asymmetric Double-Well Potential.- 9 The Swift–Hohenberg Equation.- 10 Waves in Nonlinearly Supported Beams.- References.