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 61
Page v
... linear waves . This problem is a convenient example of a non - one - dimensional boundary problem . A discrete transverse component in the wave vector allows the introduction of the concept of interacting modes . The analogy to the ...
... linear waves . This problem is a convenient example of a non - one - dimensional boundary problem . A discrete transverse component in the wave vector allows the introduction of the concept of interacting modes . The analogy to the ...
Page 2
... linear approximation the basic wave mode is intro- duced . This mode is a projection onto the eigen subspace of a Sturm - Liouville problem for transverse variables . The desired quantity w is represented by a Fourier series w = Zn ( z ) ...
... linear approximation the basic wave mode is intro- duced . This mode is a projection onto the eigen subspace of a Sturm - Liouville problem for transverse variables . The desired quantity w is represented by a Fourier series w = Zn ( z ) ...
Page 4
... linear theory . This is not a simple problem and is important for correct separation of the corresponding contributions in given initial data , a boundary regime or sources [ 1.42 ] . The approach of this book is based on a projection ...
... linear theory . This is not a simple problem and is important for correct separation of the corresponding contributions in given initial data , a boundary regime or sources [ 1.42 ] . The approach of this book is based on a projection ...
Page 5
... linear equations . Therefore it is conve- nient to preserve the traditional terminology , at least in the case of a weak non- linearity . The classification principle within the projection operators approach is general and thus allows ...
... linear equations . Therefore it is conve- nient to preserve the traditional terminology , at least in the case of a weak non- linearity . The classification principle within the projection operators approach is general and thus allows ...
Page 6
... linear problem now has a definite relation between the components of the vector , namely , v1 = { a , a } , _ = { a , -a } . Applying the operators P to ( 1.8 ) we have the system for right II = ( a - b ) / 2 and left A = ( a + b ) / 2 ...
... linear problem now has a definite relation between the components of the vector , namely , v1 = { a , a } , _ = { a , -a } . Applying the operators P to ( 1.8 ) we have the system for right II = ( a - b ) / 2 and left A = ( a + b ) / 2 ...
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