
2018 / xiv + 252 pages / Softcover / 9781611975512/ List $69.00 / SIAM Member $48.30 / Order Code: CB92
Keywords: soliton, KP equation, Grassmannian, shallow water waves, Mach reflection
Contents
Preface;
Chapter 1: Basic equations for shallow water waves;
Chapter 2: Introduction to the KP theory and the τfunction;
Chapter 3: The real Grassmannians and their parametrizations;
Chapter 4: Classification of the KP solitons;
Chapter 5: Soliton graphs;
Chapter 6: Stability and numerical simulations;
Chapter 7: The inverse problem;
Chapter 8: The Mach reflection: The Miles theory and the higher order KP theory;
Bibliography;
Index.
Weblike 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 twodimensional 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.
About the Author
Yuji Kodama is a Professor in the Department of Mathematics at The Ohio State University. His research interests are differential equations, mathematical physics, integrable systems and nonlinear PDEs, Lie algebras and field theories, applications to physical and engineering problems, and topological questions related to differential equations.
ISBN 9781611975512