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 o
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kharov System and its Soliton Solutions
The Zakharov System and its Soliton Solutions
Boling Guo Zaihui Gan Linghai Kong Jingjun Zhang •
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The Zakharov System and its Soliton Solutions
123
Boling Guo Institute of Applied Physics and Computational Mathematics Beijing China
Linghai Kong Institute of Applied Physics and Computational Mathematics Beijing China
Zaihui Gan Center for Applied Mathematics Tianjin University Tianjin China
Jingjun Zhang College of Mathematics, Physics and Information Engineering Jiaxing University Jiaxing, Zhejiang China
ISBN 978-981-10-2581-5 DOI 10.1007/978-981-10-2582-2
ISBN 978-981-10-2582-2
(eBook)
Jointly published with Science Press, Beijing Library of Congress Control Number: 2016951969 © Springer Science+Business Media Singapore and Science Press 2016 This work is subject to copyright. All rights are reserved by the Publishers, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publishers, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publishers nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #22-06/08 Gateway East, Singapore 189721, Singapore
Preface
V.E. Zakharov is a famous Russian (Soviet) mathematical physicist. He made excellent contributions to plasma physics, turbulence and soliton theory. In 1962, he considered the collapse of Langmiur waves, and in 1972, he proposed a system coupled by the electric field and the perturbation of particles when studying the interaction between plasma and laser. From the viewpoint of mathematics, such system (which was known as Zakharov system) is the nonlinear Schrödinger equation coupled with the wave equation with strong nonlinearity. Zakharov computed the soliton solution for this system, and explained clearly the unresolved phenomenon for a long time in laser target shooting, namely, the density hollow phenomenon near the critical surface. Hence, this system caused great concern among the international physics community. Since then, many research works have been done on Zakharov system
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