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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Page vi
... solitons . The derivation of NES for plasma waves requires a generalization of the method , i.e. , the expansion in small parameters of an ion distribution function . The variety of types of plasma waves that can be considered ...
... solitons . The derivation of NES for plasma waves requires a generalization of the method , i.e. , the expansion in small parameters of an ion distribution function . The variety of types of plasma waves that can be considered ...
Page 1
... soliton physics and the investigation of organized nonlinear phenomena . Examples are investigations of surface and ... solitons propagating in fiber optic waveguides [ 1.12 ] . Progress in the design of powerful sources and control ...
... soliton physics and the investigation of organized nonlinear phenomena . Examples are investigations of surface and ... solitons propagating in fiber optic waveguides [ 1.12 ] . Progress in the design of powerful sources and control ...
Page 3
... soliton solutions have been given by Hirota and Satsuma [ 1.31 ] without any discus- sion of the physical implications . The general CKdV have been derived here for different hydrodynamical systems ( Sects . 2.1-4 ) [ 1.27,32 ] . The ...
... soliton solutions have been given by Hirota and Satsuma [ 1.31 ] without any discus- sion of the physical implications . The general CKdV have been derived here for different hydrodynamical systems ( Sects . 2.1-4 ) [ 1.27,32 ] . The ...
Page 7
... solitons [ 1.51 ] . The theory of algebraic and algebro - geometric integration was developed for nonlocal dispersion in [ 1.54 ] . The soliton solutions of single mode evolution equations are generally a rather crude approximation in ...
... solitons [ 1.51 ] . The theory of algebraic and algebro - geometric integration was developed for nonlocal dispersion in [ 1.54 ] . The soliton solutions of single mode evolution equations are generally a rather crude approximation in ...
Page 10
... solitons with new properties . By the theorems given in [ 1.28 ] the Darboux transform which generalizes the Matveev ... soliton solutions of those equations are compared to the results of laboratory experiments [ 1.8 ] . We note that ...
... solitons with new properties . By the theorems given in [ 1.28 ] the Darboux transform which generalizes the Matveev ... soliton solutions of those equations are compared to the results of laboratory experiments [ 1.8 ] . We note that ...
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