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. |
From inside the book
Results 1-3 of 70
Page 7
... problem is to look for a soliton form with parameters that weakly depend on the coordinates . Knowledge of the behavior of the solutions of simplified equations allows one to apply the iteration procedure to the system considered going ...
... problem is to look for a soliton form with parameters that weakly depend on the coordinates . Knowledge of the behavior of the solutions of simplified equations allows one to apply the iteration procedure to the system considered going ...
Page 21
... problem of propagation of the system of waves is solved . One can assure himself that ( 2.30 ) coincides with the dispersion relation taken from ( 2.28 ) . The equation L ( ik ) = iw in the Fourier transform space has generally five ...
... problem of propagation of the system of waves is solved . One can assure himself that ( 2.30 ) coincides with the dispersion relation taken from ( 2.28 ) . The equation L ( ik ) = iw in the Fourier transform space has generally five ...
Page
... problem , the inverse scattering problem , dispersion relations , three - particle bound states and their scattering , collisions of particles with spin and polarization phenom- ena . The analytical properties of the scattering matrix ...
... problem , the inverse scattering problem , dispersion relations , three - particle bound states and their scattering , collisions of particles with spin and polarization phenom- ena . The analytical properties of the scattering matrix ...
Contents
Introduction | 1 |
The Discrimination and Interaction | 12 |
3 | 33 |
Copyright | |
12 other sections not shown
Other editions - View all
Common terms and phrases
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