Nonlinear Waves in Waveguides: with StratificationS.B. Leble's book deals with nonlinear waves and their propagation in metallic and dielectric waveguides and media with stratification. The underlying nonlinear evolution equations (NEEs) are derived giving also their solutions for specific situations. The reader will find new elements to the traditional approach. Various dispersion and relaxation laws for different guides are considered as well as the explicit form of projection operators, NEEs, quasi-solitons and of Darboux transforms. Special points relate to: 1. the development of a universal asymptotic method of deriving NEEs for guide propagation; 2. applications to the cases of stratified liquids, gases, solids and plasmas with various nonlinearities and dispersion laws; 3. connections between the basic problem and soliton- like solutions of the corresponding NEEs; 4. discussion of details of simple solutions in higher- order nonsingular perturbation theory. |
From inside the book
Results 1-5 of 30
Page vii
... Waves of Different Types 2.1 Hydrodynamic Wave Equations in a Three - Dimensional Stratified Medium 2.1.1 Fundamentals Atmospheric Waves : Dispersion and Polarization Projection Operators on Subspaces of Waves 2.1.2 2.2 2.2.1 2223 ...
... Waves of Different Types 2.1 Hydrodynamic Wave Equations in a Three - Dimensional Stratified Medium 2.1.1 Fundamentals Atmospheric Waves : Dispersion and Polarization Projection Operators on Subspaces of Waves 2.1.2 2.2 2.2.1 2223 ...
Page viii
... Wave Modes in Stratified Plasma 4.1.1 Description of Plasma Waves 4.1.2 Weakly Inhomogeneous Bounded Plasma Interaction of Plasma Waves 69 69 69 74 76 4.2.1 Langmuir and Ion Wave Interactions 76 4.3 4.3.1 4.2.2 Three - Wave Helico ...
... Wave Modes in Stratified Plasma 4.1.1 Description of Plasma Waves 4.1.2 Weakly Inhomogeneous Bounded Plasma Interaction of Plasma Waves 69 69 69 74 76 4.2.1 Langmuir and Ion Wave Interactions 76 4.3 4.3.1 4.2.2 Three - Wave Helico ...
Page 2
... three - dimensional nonlinear waves in guides . By means of the independent variables in the first order linear approximation the basic wave mode is intro- duced . This mode is a projection onto the eigen subspace of a Sturm - Liouville ...
... three - dimensional nonlinear waves in guides . By means of the independent variables in the first order linear approximation the basic wave mode is intro- duced . This mode is a projection onto the eigen subspace of a Sturm - Liouville ...
Page 8
... wave range . In Sects.2.2,3 the basic principles of reducing the fundamental systems of equations are demonstrated for the classic problem of Rossby and Poincaré waves . The 3 × 3 projection operators for three dispersion branches are ...
... wave range . In Sects.2.2,3 the basic principles of reducing the fundamental systems of equations are demonstrated for the classic problem of Rossby and Poincaré waves . The 3 × 3 projection operators for three dispersion branches are ...
Page 9
... three - wave resonance con- ditions are investigated in Sect . 3.2 and Appendix 4. The special problem of the resonance range of electromagnetic waves of NMR - NQR is discussed for a nuclear spin system of dielectrics ( Sect . 3.3 ) ...
... three - wave resonance con- ditions are investigated in Sect . 3.2 and Appendix 4. The special problem of the resonance range of electromagnetic waves of NMR - NQR is discussed for a nuclear spin system of dielectrics ( Sect . 3.3 ) ...
Contents
1 | |
12 | |
2223 | 19 |
5 | 30 |
6 | 37 |
7 | 45 |
88886 | 62 |
Nonlinear Waves in Stratified Plasma | 69 |
3 | 95 |
Waves in Gases Inhomogeneous in Knudsen Number | 106 |
Mean Field Generation by Waves in a Dissipative Medium | 114 |
5 | 134 |
Nonlinear Terms for Interacting Modes of Poincaré | 141 |
Basis Vectors Interaction Operator for Atomic Nuclei | 145 |
Subject Index 161 | 160 |
4 | 88 |
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Common terms and phrases
allows amplitude approximation atmosphere atmospheric waves B₁ basis functions boundary conditions calculation CKdV coefficients components contribution coordinate denote density density matrix dependence derivation described determined dielectric dimensionless dispersion branches dispersion relation dissipation distribution function dynamical variables effects electromagnetic evolution equations Fiz.Atm.Okean frequency given hydrodynamical inhomogeneity initial conditions integration internal waves ion-acoustic Ionosphere iteration KdV equation kinetic Langmuir Langmuir waves layer linear long waves magnetic field matrix mean field medium method mode interaction Moscow Nauka nonlinear constants nonlinear terms Nonlinear Waves nonlocal oscillations perturbation theory physical plasma waves problem projection operators quasisolitons region resonance Rossby waves S.B.Leble scale Sect small parameters soliton solution spectral subspaces substitution taking into account temperature thermoclyne thermoconductivity thermospheric three-wave transformed turbulence values vector velocity vertical w₁ wave propagation wave vector waveguide propagation wavelength пп