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. ContentsThe Research Process for Rogue WavesConstruction of Rogue Wave Solution by the Generalized Darboux TransformationConstruction of Rogue Wave Solution by Hirota Bilinear Method, Algebro-geometric Approach and Inverse Scattering MethodThe Rogue Wave Solution and Parameters Managing in Nonautonomous Physical Model

Table of content:Chapter 1 Introduction and updates on rogue wave research1.1 Research history and progress on rogue wave phenomenal1.2 Key experiments on rogue wave1.3 Research methods and physical mechanism of rogue wave1.4 Linear and non-linear mechanism of rogue wave1.5 Rogue wave formation; mechanism and characteristic1.6 Rogue wave simulation; experiments, statistical and numerical methods1.7 Rogue wave solution to nonlinear partial differential equation1.8 Rogue wave in optics1.9 Rogue wave in finance1.10 Rogue wave in non-autonomous systemChapter 2 Solution to rogue wave formation; generalized Darboux transformation2.1 classical Darboux transformation2.2 Darboux transformation for KdV equation2.3 Darboux transformation for NLS equation with N component2.4 Rogue wave solution to NLS equation with two component;breathers, solitons2.5 Darboux transformation for NLS equation2.6 Darboux transformation for DNLS equation; high-order solitonsChapter 3 Solutions to rogue wave formation; Bilinear transformation, algebro-geometric reduction3.1 Hirota bilinear method; solitons for NLS equation and DS-I equation3.2 Reduction for KP equation3.3 Algebro- geometric reduction; Fredholm determinant, solution to rogue wave formationChapter 4 rogue wave solution to nonlinear physical model and parameter control4.1 Introduction of rogue wave in physical studies4.2 Time-modulated NLS equation; one dimensional nonlinear physical model, symmetry analysis, solutions4.3 (3+1)-dimensional time-modulated GP/NLS equation; three dimensional nonlinear physical model, symmetry analysis4.4 Generalized time-modulated high-order NLS equation4.5 Two dimensional BEC equation4.6 (2+1)-dimensional non-local NLS equation4.7 Discrete Ablowitz-Ladik-Hirota lattices