## 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 51

Page 27

The choice of the hydrostatic approximation as the zeroth approximation

excludes the acoustic

subsystem (2.20) we bring wt to the right-hand side, including the vertical

acceleration in ...

The choice of the hydrostatic approximation as the zeroth approximation

excludes the acoustic

**contribution**[2.4]. Thus, in the third equation of the vectorsubsystem (2.20) we bring wt to the right-hand side, including the vertical

acceleration in ...

Page 66

(3.61) Supposing that the "linear" excitation conditions of a single mode

weak nonlinearity and interaction with the environment of the dielectric layer. We

choose ...

(3.61) Supposing that the "linear" excitation conditions of a single mode

**contribution**are met and a deviation from the single-mode state ft is stipulated byweak nonlinearity and interaction with the environment of the dielectric layer. We

choose ...

Page 130

Solving these equations one can derive the increment of increase in the given

spectral

may be detected, and they may be compensated for within the framework of the ...

Solving these equations one can derive the increment of increase in the given

spectral

**contributions**due to thermoconductivity. By this method the singularitiesmay be detected, and they may be compensated for within the framework of the ...

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

Introduction | 1 |

The Discrimination and Interaction | 12 |

Interaction of Modes in an Electromagnetic Field Waveguide | 50 |

Copyright | |

6 other sections not shown

### Other editions - View all

### 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