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Mathematical Surveys and Monographs
2009; 256 pp; hardcover
List Price: US$83
Member Price: US$66.40
Order Code: SURV/156
Geometric Theory of Incompressible Flows with Applications to Fluid Dynamics - Tian Ma and Shouhong Wang
Introduction to PDEs and Waves for the Atmosphere and Ocean - Andrew Majda
An Introduction to the Mathematical Theory of Waves - Roger Knobel
This book provides a self-contained presentation of classical and new methods for studying wave phenomena that are related to the existence and stability of solitary and periodic travelling wave solutions for nonlinear dispersive evolution equations. Simplicity, concrete examples, and applications are emphasized throughout in order to make the material easily accessible. The list of classical nonlinear dispersive equations studied includes Korteweg-de Vries, Benjamin-Ono, and Schrödinger equations. Many special Jacobian elliptic functions play a role in these examples.
The author brings the reader to the forefront of knowledge about some aspects of the theory and motivates future developments in this fascinating and rapidly growing field. The book can be used as an instructive study guide as well as a reference by students and mature scientists interested in nonlinear wave phenomena.
Graduate students and research mathematicians interested in nonlinear wave phenomena.
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