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This book explores the role of fractional calculus and associated partial differential equations in modeling multiscale phenomena and overlapping macroscopic & microscopic scales, offering an innovative and powerful tool for modeling complex systems. While integer order...
This book explores the impact of nonlinearity on a broad range of areas, including time-honored fields such as biology, geometry, and topology, but also modern ones such as quantum mechanics, networks, metamaterials and artificial intelligence. The concept of...
This book presents a careful selection of the most important developments of the \phi^4 model, offering a judicious summary of this model with a view to future prospects and the challenges ahead. Over the past four decades, the \phi^4 model has been the basis for...
The sine-Gordon model is a ubiquitous model of Mathematical Physics with a wide range of applications extending from coupled torsion pendula and Josephson junction arrays to gravitational and high-energy physics models.The purpose of this book is to present a summary of...
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