An Introduction to the Mathematics of Breathers: Basic Theory and Models
Author(s): Miguel Á Alejo (Author), Claudio Muñoz (Author)
Publisher Finelybook 出版社: World Scientific Publishing
Publication Date 出版日期: June 18, 2026
Language 语言: English
Print length 页数: 268 pages
ISBN-10: 9819832306
ISBN-13: 9789819832309
Book Description
The aim of this book is to introduce the mathematics of continuous breathers, one of the most beautiful mathematical and physical objects appearing in the basic description of phenomena associated with waves and dispersion. This book serves as the first instalment in this area with a rigorous flavour and attention to deep properties of breather solutions. It also intends to serve as the starting point for a theory that has developed in many directions over the past twenty years and is now under intense scrutiny and active research. Accordingly, what is presented here are the first steps — the initial results needed to understand the main goals and challenges in the study of breathers. Balancing rigor with accessibility, this text serves mathematical, physical, and computational interests. By blending geometric intuition, analysis, and explicit constructions, it highlights the complexity and elegance of breathers, offering a coherent overview and inspiration for future research.
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Editorial Reviews
About the Author
Miguel Á Alejoobtained a PhD in Mathematics in 2010 at the University of Basque Country–EHU under the guidance of Luis Vega, with postdoctoral stays during 2011–2013 at the University of Bonn and the University of Copenhagen. Moreover, during 2013–2015, he was visiting professor at IMPA. After that, during 2015–2019 he was hired as assistant professor at Federal University of Santa Catarina, Brazil. Since 2020 he was appointed at the University of Córdoba (UCO), and since 2021 he is associate professor at UCO. He is interested in Nonlinear dispersive equations, namely, well-posedness, stability and asymptotic stability of solitons, integrability but also in mathematical biology and the mathematics of deep neural networks in PDEs and quantum computing.
Claudio Muñozobtained a PhD in Mathematics in 2010 at the University of Versailles Saint-Quentin, under the advice of Yvan Martel and Frank Merle. Carlos Kenig was his postdoctoral mentor, during 2011–2013. Previously, Manuel del Pino was his undergraduate advisor at the University of Chile. Since 2013 he is Chargé de Recherche CNRS (on leave), and since 2020 he is Full Professor at DIM-CMM. He is also Principal Investigator of the Center for Mathematical Modeling CMM. He is interested in Nonlinear dispersive equations, in particular: collisions, well-posedness, stability and asymptotic stability of kinks and solitons, integrability and blow-up, and more recently, inverse problems, synergies between PDEs and number theory problems and the mathematics of deep neural networks in PDEs.
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