Rogue Waves

Rogue Waves by Boling Guo, Lixin Tian, Zhenya Yan, Liming Ling, and Yu-Feng Wang, is a research monograph discussing rogue wave solutions to the PDEs of hydrodynamics and how they are found through the Darboux and bilinear transformations. Algebro-geometric reduction, inverse scattering and similarity transformations are also presented.

The books points out that there is no one definition of a rogue wave. These waves are often characterized as a “freak wave,” “monster wave,” “extreme wave,” “killer wave,” or “giant wave.” Due to the amplitude of these waves, many ships have succumbed to them. The USA warship Ramapo in 1933 encountered the tallest recorded rogue wave at 34 meters (112 feet) in the Pacific Northwest. In 1966 the Michelangelo, a cruise ship, encountered a rogue wave 24 meters high during a voyage from Italy to the United States; it tore a hole in the ship’s superstructure. Pictures of rogue waves are on page 2 of the book along with pictures taken on the observation deck of the warship SS Spray.

In the past three decades, the development of rogue wave research has been so fast that various physical models have been proposed to describe the rogue wave phenomenon. These models include the 2011 study by N. Akhmediev, who studied the spectra of the Peregrine soliton and higher-order rational solutions for the general nonlinear Schrödinger (NLS) equation, which is used as a model in both optics and deep ocean research.

In recent years, with the developments of research on both theoretical studies and experimental observation, rogue wave phenomena have been observed in optical pulses, BEC, superfluid, atmospherics, and finance. Page 28 talks about the 2010 financial wave solutions for a nonlinear option-pricing model, which are the nonlinear wave alternative to the Black-Scholes model.

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.

Peter Olszewski is a Mathematics Lecturer at The Pennsylvania State University, The Behrend College, an editor for Larson Texts, Inc. in Erie, PA, and is the 362nd Chapter Advisor of the Pennsylvania Alpha Beta Chapter of Pi Mu Epsilon. His Research fields are in mathematics education, Cayley Color Graphs, Markov Chains, and mathematical textbooks. He can be reached at pto2@psu.edu. Webpage: www.personal.psu.edu/pto2.