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
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Page 50
In this chapter, it is shown how the nonlinear constants may be represented and
calculated in terms of a density matrix (Sect. 3.3). The boundary conditions in
metal or dielectric waveguides leads to the physically possible finite-mode case.
In this chapter, it is shown how the nonlinear constants may be represented and
calculated in terms of a density matrix (Sect. 3.3). The boundary conditions in
metal or dielectric waveguides leads to the physically possible finite-mode case.
Page 59
Matrices (A|J*|A') in the basis (3.40) have the form (3.41) The interaction operator
and the equilibrium density matrix are / 0 Hz Hz \ V = -7 \Hz 0 -iHy , f>(o) = f>(0) =
diag(0,, Q2, 1) . \Hx iHy 0 / Relaxation processes are included by the last term ...
Matrices (A|J*|A') in the basis (3.40) have the form (3.41) The interaction operator
and the equilibrium density matrix are / 0 Hz Hz \ V = -7 \Hz 0 -iHy , f>(o) = f>(0) =
diag(0,, Q2, 1) . \Hx iHy 0 / Relaxation processes are included by the last term ...
Page 145
To use the density matrix elements of (3.3) the basis for H and the interaction
operator matrix have to be constructed in this basis. In this case it is necessary to
diagonalize the operator H only in the subspace of the vectors |±), since the
vector ...
To use the density matrix elements of (3.3) the basis for H and the interaction
operator matrix have to be constructed in this basis. In this case it is necessary to
diagonalize the operator H only in the subspace of the vectors |±), since the
vector ...
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Contents
Introduction | 1 |
The Discrimination and Interaction | 12 |
Interaction of Modes in an Electromagnetic Field Waveguide | 50 |
Copyright | |
6 other sections not shown
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Common terms and phrases
allows amplitude approximation atmosphere atmospheric waveguide atmospheric waves basis functions boundary conditions calculation CKdV coefficients components considered contribution coordinate decrease denote density density matrix dependence derivation described determined dielectric dimensionless dispersion branches dispersion equation dispersion relation dissipation distribution function dynamical variables effects evolution equations exponential Fiz.Atm.Okean formulas Fourier frequency given hydrodynamical inhomogeneity initial conditions integration internal waves ion-acoustic ionospheric iteration Kaliningrad KdV equation kinetic Langmuir waves layer linear long waves magnetic field matrix mean field medium method mode interaction mode number Moscow nonlinear constants nonlinear terms Nonlinear Waves nonlocal ocean oscillations perturbation theory physical plasma waves problem projection operators quasi-waveguide quasisolitons region resonance Rossby waves S.B.Leble scale Sect small parameters soliton solution spectral SSSR stationary stratified subspaces substitution taking into account temperature thermoclyne thermoconductivity thermospheric three-wave transformed turbulence two-dimensional values velocity vertical wave interaction wave propagation wave vector waveguide propagation wavelength
Bibliographic information
| Title | Nonlinear Waves in Waveguides: with Stratification Research Reports in Physics |
| Author | Sergei B. Leble |
| Edition | illustrated |
| Publisher | Springer Berlin Heidelberg, 1991 |
| Original from | the University of California |
| Digitized | 28 May 2008 |
| ISBN | 3540521496, 9783540521495 |
| Length | 163 pages |
| Subjects | › › Science / Acoustics & Sound Science / Astronomy Science / Mechanics / Dynamics Science / Physics / Astrophysics Science / Physics / General Science / Physics / Geophysics Science / Waves & Wave Mechanics Technology & Engineering / Mechanical |
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