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. |
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Results 1-5 of 34
Page viii
... Densities of Electromagnetic 79 82 Field Fluctuations 4.3.2 One - Dimensional Turbulence 8888 82 85 4.4 Multisoliton Solutions of Discrete Silin - Tikhonchuk Equations 4.4.1 The Darboux - Matveev Transformation 5. Evolution Equations ...
... Densities of Electromagnetic 79 82 Field Fluctuations 4.3.2 One - Dimensional Turbulence 8888 82 85 4.4 Multisoliton Solutions of Discrete Silin - Tikhonchuk Equations 4.4.1 The Darboux - Matveev Transformation 5. Evolution Equations ...
Page 6
... pycnoclyne guide ( layer with density varying in z ) surrounded by infinite ho- mogeneous layers in the single mode case . For a finite - depth fluid the nonlocal KdV equation analogue has been derived by Joseph [ 1.53 6 Introduction.
... pycnoclyne guide ( layer with density varying in z ) surrounded by infinite ho- mogeneous layers in the single mode case . For a finite - depth fluid the nonlocal KdV equation analogue has been derived by Joseph [ 1.53 6 Introduction.
Page 9
... density matrix equation for the nuclear spin system ( which may be directly repeated for any n - level pseudospin system ) gives the nonlinear coupling constants as a function of transition frequencies and relaxation times . The three ...
... density matrix equation for the nuclear spin system ( which may be directly repeated for any n - level pseudospin system ) gives the nonlinear coupling constants as a function of transition frequencies and relaxation times . The three ...
Page 11
... density and maximum position variations in the F - layer of the ionosphere in terms of Whittacker functions . Details , as well as a comparison with observations of disturbances caused by the auroral current are given in [ 1.65 ] ...
... density and maximum position variations in the F - layer of the ionosphere in terms of Whittacker functions . Details , as well as a comparison with observations of disturbances caused by the auroral current are given in [ 1.65 ] ...
Page 12
... density of the medium o = m / V where m is the mass in the volume V. By the vector v we denote the mass velocity with the components v1 = Vx = U , V2 = Vy = v , v3 = Vz = w . If the medium is complex and can be described by the ...
... density of the medium o = m / V where m is the mass in the volume V. By the vector v we denote the mass velocity with the components v1 = Vx = U , V2 = Vy = v , v3 = Vz = w . If the medium is complex and can be described by the ...
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