A study of nonlinear higher order model equations central to the description and analysis of spatio-temporal pattern formation in the natural sciences. Unique combination of results obtained by rigorous mathematical analysis and computational studies. Text exhibits the principal families of solutions--kinks, pulses and periodic solutions, and their dependence on critical eigenvalue parameters. Exposition first focuses on a single equation to achieve optimal transparency, then branches out to wider classes of equations. Includes many exercises, open problems, recent original results, and applications to mathematical physics and mechanics. Intended for mathematicians, mathematical physicists, and graduate students.

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"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

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