The Zakharov System and its Soliton Solutions 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. . Physical background of Zakharov equations and its soliton solutions On the existence blowup and large time behavior of the Zakharov system Studies on generalized Zakharov system Low regularity theories of Zakharov system Singular limit of Klein Gordon Zakharov system with infinite propagation speed. .