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 64
... amplitude . By finding the soliton contribution and by measuring the amplitude , one can determine the nonlinear constants ẞ ; and therefore the relaxation times Tik . The parameters of the solution ( 3.53 ) are related among themselves ...
... amplitude . By finding the soliton contribution and by measuring the amplitude , one can determine the nonlinear constants ẞ ; and therefore the relaxation times Tik . The parameters of the solution ( 3.53 ) are related among themselves ...
Page 125
... amplitude with multiple sin 21 that depends on the magnetic inclination to the characteristic diffusion rate μ / T at the lower boundary of the thermosphere . The second one contains the amplitude σ and the dispersion parameter A / A ...
... amplitude with multiple sin 21 that depends on the magnetic inclination to the characteristic diffusion rate μ / T at the lower boundary of the thermosphere . The second one contains the amplitude σ and the dispersion parameter A / A ...
Page 136
... amplitude ã . Using ( 6.63 ) we set the mode energy and the energy loss in a period equal , i.e. , we shall assume that there is an approximate equilibrium between them that is reached at the amplitude ã . Due to ( 6.63 ) we have Tindz ...
... amplitude ã . Using ( 6.63 ) we set the mode energy and the energy loss in a period equal , i.e. , we shall assume that there is an approximate equilibrium between them that is reached at the amplitude ã . Due to ( 6.63 ) we have Tindz ...
Contents
Introduction | 1 |
The Discrimination and Interaction | 12 |
3 | 33 |
Copyright | |
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amplitude approximation atmosphere B₁ boundary conditions calculation CKdV coefficients components contribution coordinate denote density density matrix dependence derivation described determined dielectric dimensionless dispersion branches dispersion equation dispersion relation dissipation distribution function dynamical variables effects electromagnetic electron evolution equations frequency given group velocities H₂ hydrodynamical inhomogeneity initial conditions integration internal waves ion-acoustic waves ionospheric iteration KdV equation kinetic Langmuir wave layer linear longitudinal longitudinal waves magnetic field matrix mean field medium method mode interaction nonlinear constants nonlinear terms Nonlinear Waves nonlocal oscillations particles perturbation theory physical plasma waves problem projection operators quasisolitons region resonance Rossby waves S.B.Leble scale Sect small parameters soliton solution spectral SSSR stationary subspaces substitution taking into account temperature thermoclyne thermoconductivity thermospheric three-wave transformed turbulence velocity vertical w₁ wave propagation wave vector waveguide propagation wavelength