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 56
Page 2
... us turn to the role of the boundary conditions that determine the basic functions Zn for the expansion ( 1.1 ) . In the simple cases of classic waveguides , these are the uniform conditions that give the standard spectral 2 Introduction.
... us turn to the role of the boundary conditions that determine the basic functions Zn for the expansion ( 1.1 ) . In the simple cases of classic waveguides , these are the uniform conditions that give the standard spectral 2 Introduction.
Page 4
... determination ( i.e , separation of waves according to their types ) . The formulation of this problem appeared in the pioneering work [ 1.6 ] in a search for a connection between the solutions of Boussinesq and KdV equations . The ...
... determination ( i.e , separation of waves according to their types ) . The formulation of this problem appeared in the pioneering work [ 1.6 ] in a search for a connection between the solutions of Boussinesq and KdV equations . The ...
Page 6
... determined too . The complexity of the wave separation problem depends on the number of dynamical variables and orders of derivatives in the equations of the fundamental problem . The separation into right- and left - travelling waves ...
... determined too . The complexity of the wave separation problem depends on the number of dynamical variables and orders of derivatives in the equations of the fundamental problem . The separation into right- and left - travelling waves ...
Page 11
... determine the interaction between a shear flow and internal waves are derived ( see also Appendix 5 ) . Large ... determination of the transport coefficients including background turbulence [ 1.84 ] . As a result of the internal wave ...
... determine the interaction between a shear flow and internal waves are derived ( see also Appendix 5 ) . Large ... determination of the transport coefficients including background turbulence [ 1.84 ] . As a result of the internal wave ...
Page 12
... determination of the ground state is nontrivial . The assumption of stationarity is to some degree arbitrary and requires justification . Indeed , in experiments , large scale motion is regarded as a background phe- nomenon but the ...
... determination of the ground state is nontrivial . The assumption of stationarity is to some degree arbitrary and requires justification . Indeed , in experiments , large scale motion is regarded as a background phe- nomenon but the ...
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