The Zakharov System and its Soliton Solutions

Description

This book focuses on the theory of the Zakharov system in the context of plasma physics. It has been over 40 years since the system was first derived by V. E. Zakharov – and in the course of those decades, many innovative achievements with major impacts on other research fields have been made. The book represents a first attempt to highlight the mathematical theories that are most important to researchers, including the existence and unique problems, blow-up, low regularity, large time behavior and the singular limit. Rather than attempting to examine every aspect of the Zakharov system in detail, it provides an effective road map to help readers access the frontier of studies on this system.   Front Matter....Pages i-ix Physical Background of Zakharov Equations and Its Soliton Solutions....Pages 1-20 On the Existence, Blowup and Large Time Behavior of the Zakharov System....Pages 21-127 Studies on Generalized Zakharov System....Pages 129-215 Low Regularity Theories of Zakharov System....Pages 217-291 Singular Limit of Klein–Gordon–Zakharov System with Infinite Propagation Speed....Pages 293-334 Back Matter....Pages 335-342