Nonlinear Water Waves

This monograph is the first to summarize the research on nonlinear wave phenomena over the past three decades, and it also presents numerous applications in physics, geophysics, and engineering.

Audience: Graduate, post-graduate students, researchers and practitioners in applied mathematics, physics, geophysics, civil, mechanical and electrical engineering. Excellent for library markets, since this one volume will be the first of its kind to summarize the state of literature on nonlinear water waves over the past three decades.

Wave motion in water is one of the most striking observable phenomena in nature. Throughout the twentieth century, development of the linearized theory of wave motion in fluids and hydrodynamic stability has been steady and significant. In the last three decades there have been remarkable developments in nonlinear dispersive waves in general, nonlinear water waves in particular, and nonlinear instability phenomena. New solutions are now available for waves modulatedin both space and time, which exhibit new phenomena as diverse as solitons, resonant interactions, side-band instability, and wave-breaking. Other achievements include the discovery of soliton interactions, and the Inverse Scattering Transform method forfinding the explicit exact solution for several canonical nonlinear partial differential equations.

This monograph is the first to summarize the research on nonlinear wave phenomena over the past three decades, and it also presents numerous applications in physics, geophysics, and engineering.

Booknews

Based on the author's lecture notes for an evolving series of lectures on linear and nonlinear water waves at the U. of Calcutta between 1969 and 1981, this volume provides a coherent account of the recent developments in nonlinear water waves in eight chapters: basic equations of motion of inviscid and viscous fluids; the theory of surface waves on water; transient wave motions in an inviscid fluid; nonlinear shallow water waves and solitons; ship waves and wave resistance; nonlinear diffraction of water waves; the theory of nonlinear dispersive waves; and nonlinear instability of dispersive waves with applications to water waves. Annotation c. Book News, Inc., Portland, OR (booknews.com)

Lokenath Debnath is Professor of the Department of Mathematics and Professor of Mechanical and Aerospace Engineering at the University of Central Florida in Orlando. He received his M.Sc. and Ph.D. degrees in pure mathematics from the University of Calcutta, and obtained D.I.C. and Ph.D. degrees in applied mathematics from the Imperial College of Science and Technology, University of London. He was a Senior Research Fellow at the University of Cambridge and has had visiting appointments to several universities in the United States and abroad. His many honors and awards include two Senior Fulbright Fellowships and an NSF Scientist award to visit India for lectures and research. Dr. Debnath is author or co-author of several books and research papers in pure and applied mathematics, and serves on several editorial boards for scientific journals. He is the current and founding Managing Editor of the International Journal of Mathematics and Mathematical Sciences.