●1Physical Background of Zakharov Equations and Its Sollton Solutions
1.1Transport Process in a Plasma
1.2System of Equations for Two-Fluid Dynamics
1.3Solitons in Plasmas
1.3.1Soliton in Ion Acoustic Wave
1.3.2 Langmuir Soliton
1.3.3Ls Soliton
1.3.4 The Light Soliton
1.3.5Solitons of Simplified Two-Fluid System
2On the Existence, Blowup and Large Time Behavior of the Zakharov System
2.1Existence and Uniqueness Theory of the Zakharov System
2.1.1Weak Solution Theory of Zakharov System
2.1.2Local Smooth Solution to Zakharov System
2.1.3Global Smooth Solution to Zakharov System
2.2Blowup Phenomenon of the Zakharov System
2.2.1Existence of Self-Similar Blowup Solutions to Zakharov System
2.2.2Auxiliary Propositions and Lemmas
2.2.3Existence and Uniqueness of Radially Symmetric Solutions
2.2.4Concentration Phenomenon of the Blowup Solutions
2.2.5Nonexistence of Blowup Solutions with Minimum Mass
2.3Scattering for the Zakharov System in 3D
2.3.1Reduction of the System and Linear Decay Estimates
2.3.2 Energy Estimate
2.3.3Decay Estimate for the Wave Equation
2.3.4Weighted Estimates for the Wave Component
2.3.5Weighted Estimates for the Schr6dinger Component
2.4Global Attractors of Dissipative Zakharov System
2.4.1Uniform a Priori Estimates
2.4.2Existence of Global Attractor
3Studies on Generalized Zakharov System
3.1Zakharov System in Northomogeneous Medium
3.1.IA Priori Estimates
3.1.2Existence and Uniqueness of Global Smooth Solutions
3.2Klein--Gordon-Zakharov System
3.3Zakharov System in Two Dimensional Ion-Acoustic Waves
3.4Zakharov Systems with Magnetic Field Effect
3.4.1Reduction of Zakharov System with a Magnetic Field
3.4.2Conservation Laws and Existence of Weak Solutions
3.4.3Regularized System for the Magnetic Zakharov System
3.4.4Local Existence Theory of Zakharov System in Cold Plasmas
3.4.5Local Existence Theory for Zakharov System in Hot Plasmas
3.4.6Global Existence of Smooth Solutions
3.4.7Convergence Behavior of Zakharov System with Magnetic Field Effect
3.5Global Well- edness for the Quantum Zakharov System
3.5.1The Main Results
3.5.2Some Energy Estimates for the Solution
3.5.3Proof of the Global Well- edness Result
3.5.4Proof of the Classic Limit Behavior
4Low Regularity Theories of Zakharov System
4.1Preliminaries
4.1.1Work Space
4.1.2Linear Estimates
4.2Global Well- edness for One Dimensional Zakharov System
4.2.1Main Results and Introduction of the Strategy
4.2.2Estimates for Groups and Duhamel Terms
4.2.3Proof of Global Well- edness
4.2.4 ltilinear Estimates
4.3Low Regularity for Zakharov System in Higher Dimension
4.3.1Reduction of the System
4.3.2Estimates of Nonlinear Terms
4.3.3Well- edness of Zakharov System in Higher Dimensions
4.4 Well- edness of Two Dimensional Zakharov System
4.4.1Local Well- edness Result
4.4.2Proof of the Main Theorem
4.4.3Proof of ltilinear Estimates
5Singular Limit of Klein--Gordon-Zakharov System with Infinite Propagation Speed
5.1Introduction
5.2Preliminary Knowledge
5.2.1Notations and the Frequency Decomposition
5.2.2 Local WeU- edness Result
5.2.3Reduction of the System
5.2.4Strichartz Norms, Fourier Restriction Norms
and Related Estimates
5.3Bilinear Estimates for Regular Interactions and Non-resonant Interactions
5.4 Energy Estimate on the Resonant Components
5.5Convergence Results
5.5.1Limit Behavior of the Klein-Gordon-Zakharov System
5.5.2Uniform Bounds and Two Lemmas
5.6Proof of the Main Results
5.7Convergence in the Energy Space with Small Initial Data
References

Zakharov方程是描述激光與等離子體相互作用的一類非常重要的非線性作用方程組，這類方程具有廣泛的物理和應用背景。本書利用雙流體力學方程組詳細地推導出了Zakharov方程，還給出不同類型的等離子體孤立子。本書著重研究幾種重要類型的Zakharov方程在能量空間中的一些經典結果，其中包括一維及高維問題的適定性結果、爆破問題和長時間行為、高維非均勻介質中的Zakharov方程、Klein-Gordon-Zakharov方程、離子聲Zakharov方程及磁場Zakharov方程的相關數學理論研究成果。利用調和分析的現代理論和方法，本書詳細介紹此類方程的低正則性結果，以及Zakharov型方程當離子體傳播速度及電場傳播速度趨於無窮時的奇性極限。