This book provides a clear and systematic introduction to solitons, spanning foundational theory, analytical techniques and physical applications. It begins with classical models such as the KdV and nonlinear Schrödinger equations, then develops key elements including the inverse scattering transform, Hirota method, Bäcklund transformations, infinite conservation laws, and multidimensional soliton theory. The work explores asymptotic behavior, stability, numerical approaches, and topological structures, while also addressing the geometry of solitons, global-solution problems, and blow-up phenomena. A dedicated chapter examines rogue waves and wave turbulence, and recent advances are highlighted through applications in condensed-matter physics. Balancing rigorous analysis with physical insight, this book serves both as a valuable reference for researchers and graduate students and as a lucid introduction for newcomers to the field.

Contributor: Boling GUO

Boling GUO is a Member of the Chinese Academy of Sciences (CAS) and researcher at the Beijing Institute of Applied Physics and Computational Mathematics. His research interests include nonlinear evolution equations, soliton theory, infinite-dimensional dynamical systems, stochastic infinite-dimensional dynamical systems, and fractional partial differential equations. He has authored more than 800 journal papers and over 10 books.