This book gives an overview of the theoretical research on rogue waves and discusses solutions to rogue wave formation via the Darboux and bilinear transformations, algebro-geometric reduction, and inverse scattering and similarity transformations. Studies on nonlinear optics are included, making the book a comprehensive reference for researchers in applied mathematics, optical physics, geophysics, and ocean engineering.
Contents
The Research Process for Rogue Waves
Construction of Rogue Wave Solution by the Generalized Darboux Transformation
Construction of Rogue Wave Solution by Hirota Bilinear Method, Algebro-geometric Approach and Inverse Scattering Method
The Rogue Wave Solution and Parameters Managing in Nonautonomous Physical Model
Contents
The Research Process for Rogue Waves
Construction of Rogue Wave Solution by the Generalized Darboux Transformation
Construction of Rogue Wave Solution by Hirota Bilinear Method, Algebro-geometric Approach and Inverse Scattering Method
The Rogue Wave Solution and Parameters Managing in Nonautonomous Physical Model
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"The book is a research monograph that provides the reader with the observation that rogue waves can be modeled by PDEs describing fluid motion. It is a comprehensive resource for researchers in the applied mathematics, optical physics, geophysics, and ocean engineering fields." MAA Reviews
"After reviewing the physical mechanisms behind rouge waves the present monograph discusses the construction of explicit solutions corresponding to such waves for a large number of important models using Darboux-type transformations, the Hirota bilinear method, the algebro-geometric approach and the inverse scattering transform. In addition it contains an overview of the current literature (both theoretical and experimental) on this topic. The presentation is aimed at researchers working in applied mathematics and engineering."
G. Teschl in: Monatshefte für Mathematik 190 (2019), 210
"After reviewing the physical mechanisms behind rouge waves the present monograph discusses the construction of explicit solutions corresponding to such waves for a large number of important models using Darboux-type transformations, the Hirota bilinear method, the algebro-geometric approach and the inverse scattering transform. In addition it contains an overview of the current literature (both theoretical and experimental) on this topic. The presentation is aimed at researchers working in applied mathematics and engineering."
G. Teschl in: Monatshefte für Mathematik 190 (2019), 210