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 56
Page ix
... Interaction Operator for Atomic Nuclei with Spin 1 Appendix 5 Nonlinear Internal Waves and Shear Flow Interaction Constants References Subject Index 145 148 151 161 1. Introduction We shall first give some general remarks related.
... Interaction Operator for Atomic Nuclei with Spin 1 Appendix 5 Nonlinear Internal Waves and Shear Flow Interaction Constants References Subject Index 145 148 151 161 1. Introduction We shall first give some general remarks related.
Page 2
... nonlinear wave theory is not at all complete . The propagation of waves in ... nonlinear equations - Korteweg - de Vries ( KdV ) , Kadomtsev - Petviashvili ... constants . The parameters σ , ß characterize the amplitude and scale of an ...
... nonlinear wave theory is not at all complete . The propagation of waves in ... nonlinear equations - Korteweg - de Vries ( KdV ) , Kadomtsev - Petviashvili ... constants . The parameters σ , ß characterize the amplitude and scale of an ...
Page 3
... nonlinear and dispersion constants was obtained . In a collaboration with Kshevetsky the approach to CKdV integration was developed . This allows one to reduce the wave disturbance solution , which is nearly a single - mode wave , to ...
... nonlinear and dispersion constants was obtained . In a collaboration with Kshevetsky the approach to CKdV integration was developed . This allows one to reduce the wave disturbance solution , which is nearly a single - mode wave , to ...
Page 8
... nonlinear and dispersion terms . Detailed expressions are given for interaction constants in the long wave range . It is shown that nonlinear dispersion of long Rossby waves is described by a generalized CKdV equation [ 1.29,30 ] ...
... nonlinear and dispersion terms . Detailed expressions are given for interaction constants in the long wave range . It is shown that nonlinear dispersion of long Rossby waves is described by a generalized CKdV equation [ 1.29,30 ] ...
Page 9
... constants that are numerically calculated and tabulated with explicit formulas . The signs of the nonlinear terms of triads correspond to the nonlinear explo- sion instability . The corresponding periods are compared with experimental ...
... constants that are numerically calculated and tabulated with explicit formulas . The signs of the nonlinear terms of triads correspond to the nonlinear explo- sion instability . The corresponding periods are compared with experimental ...
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