Rogue waves (also called freak waves or monster waves) are an interesting topic which was first studied and investigated in hydrodynamics.
In this book, the authors describe different mathematical techniques to deal with rogue waves, and give a number of applications. They emphasize the mathematical techniques and all the calculations are done in detail. Not only rogue water waves are discussed, but also optical rogues waves and rogue waves in finance are considered. The mathematical techniques utilized such as the Darboux transform and the Hirota bilinear method are described.
Chapter 1 provides a survey on the research in rogue waves, considering not only rogue waves in hydrodynamics, but also in optics and finance. The construction of rogue waves by the generalized Darboux transform is described in Chapter 2. In this context, the Korteweg de Vries equation and the nonlinear Schrödinger equation in one, two and three space dimensions are investigated. The Hirota bilinear method is introduced in Chapter 3 and utilized for the construction of rogue waves. Similarity reductions of the partial differential equations and inverse scattering are also discussed. Chapter 4 discusses a number of applications not only in hydrodynamics, but also optical rogue waves and two-dimensional binary mixtures of Bose-Einstein condensates.
This book is a welcome addition to this topic.