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 1-3 of 26
Page 8
... dissipation is discussed . It is noted that the condition div v = 0 contradicts the energy equation with a nonzero thermoconductivity term . This point , which was neglected in [ 1.26 ] , has corollaries in the mean field generation ...
... dissipation is discussed . It is noted that the condition div v = 0 contradicts the energy equation with a nonzero thermoconductivity term . This point , which was neglected in [ 1.26 ] , has corollaries in the mean field generation ...
Page 36
... dissipation cannot compensate for the increasing steepness in the horizontal profile . This is due to Hk , < 1 and the dissipation contribution mainly depends on the vertical wave structure . The compensation for the nonlinear increase ...
... dissipation cannot compensate for the increasing steepness in the horizontal profile . This is due to Hk , < 1 and the dissipation contribution mainly depends on the vertical wave structure . The compensation for the nonlinear increase ...
Page 114
... dissipation and diffusion effects in the presence of waves ( Sect . 6.1 ) . We relate dissipation to the mean field which is generated by the medium perturbation in the range of zero wavenumber that appears due to resonant nonlinear ...
... dissipation and diffusion effects in the presence of waves ( Sect . 6.1 ) . We relate dissipation to the mean field which is generated by the medium perturbation in the range of zero wavenumber that appears due to resonant nonlinear ...
Contents
Introduction | 1 |
The Discrimination and Interaction | 12 |
3 | 33 |
Copyright | |
12 other sections not shown
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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