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 33
Page v
... modes . The analogy to the Bubnov- Galerkin method and the approximate description of finite number level in quan- tum mechanics can also be shown . The projection procedure with mode expansion allows to represent the nonlinear ...
... modes . The analogy to the Bubnov- Galerkin method and the approximate description of finite number level in quan- tum mechanics can also be shown . The projection procedure with mode expansion allows to represent the nonlinear ...
Page viii
... Modes in Stratified Plasma 4.1.1 Description of Plasma Waves 4.1.2 Weakly ... Number 106 6. Mean Field Generation by Waves in a Dissipative Medium 114 6.1 ... Modes of Poincaré and Rossby Waves at a Rotating Channel Surface 141 Appendix 3 ...
... Modes in Stratified Plasma 4.1.1 Description of Plasma Waves 4.1.2 Weakly ... Number 106 6. Mean Field Generation by Waves in a Dissipative Medium 114 6.1 ... Modes of Poincaré and Rossby Waves at a Rotating Channel Surface 141 Appendix 3 ...
Page 3
... mode generalization . Separating the propagation medium into regions of ... modes was continued by Miropolsky [ 1.26 ] , Pelinovsky [ 1.25 ] and this author ... number n , so that convergence of the expansion ( 1.1 ) is obtained . In ...
... mode generalization . Separating the propagation medium into regions of ... modes was continued by Miropolsky [ 1.26 ] , Pelinovsky [ 1.25 ] and this author ... number n , so that convergence of the expansion ( 1.1 ) is obtained . In ...
Page 6
... number of dynamical variables and orders of derivatives in the equations of ... mode expansion due to simplification of the structure of the basic equation ... mode case . For a finite - depth fluid the nonlocal KdV equation analogue has ...
... number of dynamical variables and orders of derivatives in the equations of ... mode expansion due to simplification of the structure of the basic equation ... mode case . For a finite - depth fluid the nonlocal KdV equation analogue has ...
Page 10
... mode system for internal pycnoclyne waves is shown . For a single mode the system yields the equation that unites ... number ( Kn ) [ 1.77 ] . The results of sound propagation investi- gations at arbitrary Kn are reported in [ 1.78 ] and ...
... mode system for internal pycnoclyne waves is shown . For a single mode the system yields the equation that unites ... number ( Kn ) [ 1.77 ] . The results of sound propagation investi- gations at arbitrary Kn are reported in [ 1.78 ] and ...
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