Applications of Lie Group Analysis in Geophysical Fluid Dynamics - Couverture rigide

Ibragimov, Nail H; Ibragimov, Ranis N

 
9789814340465: Applications of Lie Group Analysis in Geophysical Fluid Dynamics
Couverture rigide
ISBN 10 : 9814340464 ISBN 13 : 9789814340465
Editeur : World Scientific Publishing Co Pte Ltd, 2011

Synopsis

This is the first monograph dealing with the applications of the Lie group analysis to the modeling equations governing internal wave propagation in the deep ocean. A new approach to describe the nonlinear interactions of internal waves in the ocean is presented. While the central idea of the book is to investigate oceanic internal waves through the prism of Lie group analysis, it is also shown for the first time that internal wave beams, representing exact solutions to the equation of motion of stratified fluid, can be found by solving the given model as invariant solutions of nonlinear equations of motion. On the illustrative basis, it is also shown that the presence of the invariant solutions makes it possible to construct a more general class of disturbances, which represent wave beams propagating in certain direction coinciding with the beam energy. This book is designed for specialists in Geophysical Fluid Dynamics, Ocean and Atmospheric Modeling, as well as for researchers, teachers and students - mathematicians and nonmathematicians - interested in methods of applied group analysis for investigating nonlinear problems in physical, engineering and natural sciences. It can also serve as a textbook on practical applications of symmetries of nonlinear differential equations for graduate students in applied mathematics, physics and engineering.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

This is the first monograph dealing with the applications of the Lie group analysis to the modeling equations governing internal wave propagation in the deep ocean. A new approach to describe the nonlinear interactions of internal waves in the ocean is presented. While the central idea of the book is to investigate oceanic internal waves through the prism of Lie group analysis, it is also shown for the first time that internal wave beams, representing exact solutions to the equation of motion of stratified fluid, can be found by solving the given model as invariant solutions of nonlinear equations of motion. On the illustrative basis, it is also shown that the presence of the invariant solutions makes it possible to construct a more general class of disturbances, which represent wave beams propagating in certain direction coinciding with the beam energy. This book is designed for specialists in Geophysical Fluid Dynamics, Ocean and Atmospheric Modeling, as well as for researchers, teachers and students - mathematicians and nonmathematicians - interested in methods of applied group analysis for investigating nonlinear problems in physical, engineering and natural sciences. It can also serve as a textbook on practical applications of symmetries of nonlinear differential equations for graduate students in applied mathematics, physics and engineering.

Revue de presse

The book can be recommended for readers interested in applications of Lie transformation groups to geophysical fluid dynamics and also for beginners looking for an easy and gentle introduction to these techniques. --Zentralblatt MATH

The book is rather well written and should be interesting to a broad spectrum of researchers, teachers and students; ocean physicists, atmosphere physicists and applied mathematicians. I am deeply convinced that the book will inspire some ambitious explorers to new ideas in geophysical fluid dynamics. --Pure and Applied Geophysics

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
World Scientific Publishing Co Pte Ltd
Date d'édition
2011
Langue
anglais
ISBN 10 
9814340464
ISBN 13 
9789814340465
Reliure
Relié
Nombre de pages
228
Coordonnées du fabricant
non disponible
Personne responsable
non disponible