This self-contained set of lectures addresses a gap in the literature by providing a systematic
link between the theoretical foundations of the subject matter and cutting-edge applications in
both geophysical fluid dynamics and nonlinear optics. Rogue and shock waves are phenomena that
may occur in the propagation of waves in any nonlinear dispersive medium. Accordingly they
have been observed in disparate settings - as ocean waves in nonlinear optics in
Bose-Einstein condensates and in plasmas. Rogue and dispersive shock waves are both
characterized by the development of extremes: for the former the wave amplitude becomes
unusually large while for the latter gradients reach extreme values. Both aspects strongly
influence the statistical properties of the wave propagation and are thus considered together
here in terms of their underlying theoretical treatment. This book offers a self-contained
graduate-level text intended as both an introduction and reference guide for a new generation
of scientists working on rogue and shock wave phenomena across a broad range of fields in
applied physics and geophysics.
