## Nonlinear waves in waveguides: with stratification |

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Page 47

The basic three-wave interaction is the main

nonlinearity. Denoting and using linear relations between variables in the

nonlinear expression (Sect. 2.5), we can write the full equation m' ,u' -^X'^Al)(^. (

2.104) Let us ...

The basic three-wave interaction is the main

**resonance**for the quadraticnonlinearity. Denoting and using linear relations between variables in the

nonlinear expression (Sect. 2.5), we can write the full equation m' ,u' -^X'^Al)(^. (

2.104) Let us ...

Page 61

As follows from the derived formulas, e.g., (3.45), the intermode interaction effect

is

field u coincides with the transition frequency of the medium, the quantum system

, ...

As follows from the derived formulas, e.g., (3.45), the intermode interaction effect

is

**resonant**in the usual sense of the word: when the frequency of the externalfield u coincides with the transition frequency of the medium, the quantum system

, ...

Page 163

... 123 Rectangular waveguide with conducting walls 52 Relaxation process 59

Relaxation time approximation 108, 112

nonlinear interaction 114,133 Riemann theta-function 33, 34 Right(left)-travelling

wave 5, ...

... 123 Rectangular waveguide with conducting walls 52 Relaxation process 59

Relaxation time approximation 108, 112

**Resonance**triads 47**Resonant**nonlinear interaction 114,133 Riemann theta-function 33, 34 Right(left)-travelling

wave 5, ...

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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 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 S.BXeble 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