Nonlinear Physics, from Vibration Control to Rogue Waves and Beyond
This textbook is devoted to nonlinear physics, using the asymptotic perturbation method as a mathematical tool. The theory is developed systematically, starting with nonlinear oscillators, limit cycles and their bifurcations, followed by iterated nonlinear maps, continuous systems, nonlinear partial differential equations (NPDEs) and culminating with infinite-period bifurcation in the nonlinear Schrodinger equation and fractal and chaotic solutions in NPDEs.
A remarkable feature of the book is its emphasis on applications. It offers several examples, and the scientific background is explained at an elementary level and closely integrated with the mathematical theory. In addition, it is ideal for an introductory course at the senior or first-year graduate level.
Attilio Maccari is a freelance researcher of nonlinear physics. He received his PhD from La Sapienza Rome University, Italy in 1990. He has published about 100 papers, mainly on coupled oscillators and nonlinear partial differential equations in physics and engineering. His recent work has been devoted to vibration control, and he found two new methods in order to perform this very important task: a time delay state feedback control and a nonlocal feedback control.
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