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 41
Page vi
... perturbation theory is applied just as in the NES derivation . The author is indebted to the Leningrad State University for providing the possibility to contemplate and discuss the principal features of these investiga- tions . The ...
... perturbation theory is applied just as in the NES derivation . The author is indebted to the Leningrad State University for providing the possibility to contemplate and discuss the principal features of these investiga- tions . The ...
Page viii
... Perturbation Theory 132 6.5 Mean Field Generation in a Dissipative Medium and Fine Structure of the Oceanic Thermoclyne 135 Appendix 1 Atmospheric Waves over a Rotating Planet 139 Appendix 2 Nonlinear Terms for Interacting Modes of ...
... Perturbation Theory 132 6.5 Mean Field Generation in a Dissipative Medium and Fine Structure of the Oceanic Thermoclyne 135 Appendix 1 Atmospheric Waves over a Rotating Planet 139 Appendix 2 Nonlinear Terms for Interacting Modes of ...
Page 3
... perturbation theory to nonlinear os- cillations began with the well - known works of A.Poincaré , N.N.Bogolyubov and B.G.Galerkin . The generalization of their results was done by Taniuti [ 1.16–19 ] , Maslov , Dobrokhotov [ 1.20-22 ] ...
... perturbation theory to nonlinear os- cillations began with the well - known works of A.Poincaré , N.N.Bogolyubov and B.G.Galerkin . The generalization of their results was done by Taniuti [ 1.16–19 ] , Maslov , Dobrokhotov [ 1.20-22 ] ...
Page 4
... perturbation scheme . The analysis of the solution demonstrates the tendency ... theory of integrable systems [ 1.37 ] as well as the discovery of integrable ... theory . This is not a simple problem and is important for correct ...
... perturbation scheme . The analysis of the solution demonstrates the tendency ... theory of integrable systems [ 1.37 ] as well as the discovery of integrable ... theory . This is not a simple problem and is important for correct ...
Page 6
... perturbation method [ 1.44 ] as it is shown for the nonlinear string case ... theory of integrable systems often lead to the proposal of new equations and ... theory of electro- magnetic wave dispersion are introduced when spatial ...
... perturbation method [ 1.44 ] as it is shown for the nonlinear string case ... theory of integrable systems often lead to the proposal of new equations and ... theory of electro- magnetic wave dispersion are introduced when spatial ...
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