Nonlinear water waves with applications to wave-current interactions and tsunamis. (English) Zbl 1266.76002

Constantin, Adrian

CBMS-NSF Regional Conference Series in Applied Mathematics 81. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM) (ISBN 978-1-611971-86-6/pbk; 978-1-611971-87-3/ebook). xii, 321 p. (2011).

The book presents a mathematical analysis of a set of problems from the standard and more modern water-wave theory, selected by the author according to his research interests. Particular chapters deal with wave-current interactions, the kinematic description of wavetrains, solitons, wave-breaking dynamics, and the modeling of tsunamis. The presentation is given in a rather rigorous (formal) mathematical style, but physical motivations are considered, too, and experimental data and observations for such phenomena as wave breaking, solitons, tsunamis, etc., are also included.

Reviewer: Boris A. Malomed (Tel Aviv)

MSC:

76-02	Research exposition (monographs, survey articles) pertaining to fluid mechanics
76B15	Water waves, gravity waves; dispersion and scattering, nonlinear interaction
76B25	Solitary waves for incompressible inviscid fluids
86A05	Hydrology, hydrography, oceanography
35Q35	PDEs in connection with fluid mechanics

Keywords:

wavetrain; soliton; wave breaking