Includes bibliographical references (pages 241-250) and index.
Contents:
Basic equations for shallow water waves -- Introduction to the KP theory and the t-function -- The real Grassmannians and their parametrizations -- Classification of the KP solitons -- Soliton graphs -- Stability and numerical simulations -- The inverse problem -- The Mach reflection : the miles theory and the higher order KP theory.
Summary:
"Web-like waves, often observed on the surface of shallow water, are examples of nonlinear waves. They are generated by nonlinear interactions among several obliquely propagating solitary waves, also known as solitons. In this book, modern mathematical tools--algebraic geometry, algebraic combinatorics, and representation theory, among others--are used to analyze these two-dimensional wave patterns. The author's primary goal is to explain some details of the classification problem of the soliton solutions of the KP equation (or KP solitons) and their applications to shallow water waves. This book is intended for researchers and graduate students." --Publisher's description.
Series:
CBMS-NSF regional conference series in applied mathematics ; 92
This resource is supported by the Institute of Museum and Library Services under the provisions of the Library Services and Technology Act as administered by State Library of Iowa.