Rogue Waves In Integrable Systems Bo Yang Jianke Yang by Bo Yang, Jianke Yang 9783031667923, 3031667921 instant download after payment.

physically important integrable systems. The first chapter derives many of these

integrable systems in physical settings such as water waves, optics, and plasma.

This chapter provides physical motivations for our mathematical studies in later

chapters. The second chapter derives rogue wave solutions in a wide array of

integrable systems, including those obtained in Chap. 1 and much beyond. In

the literature, rogue waves in many of those integrable systems were originally

derived by generalized Darboux transformation. We will derive these rogue waves

almost exclusively by the bilinear method, since rogue wave expressions by the

bilinear method are much more explicit than those by Darboux transformation. The

third chapter analyzes patterns of rogue waves in certain asymptotic limits such as

large internal parameters. Connections between rogue patterns and root structures

of special polynomials will be revealed, and universality of these rogue patterns

in integrable systems will be established. The fourth chapter describes laboratory

experiments on rogue waves in physical settings such as optical fibers, water tanks,

plasma, and BEC. The last chapter covers topics that are closely related to rogue

waves of the earlier chapters, such as rogue waves arising from a nonuniform

background, robustness of rogue waves, partial-rogue waves, and lump patterns in

the Kadomtsev-Petviashvili I equation.