## Nonlinear waves in waveguides: with stratification |

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Page 30

The function F contains both

and Coriolis terms K, F = N + D + K, where for K see (A 1.3) and the main part of

D in small parameters is p1 Pi D = -Ttttt tA^Tu + vo[u utz + (v- uz)uz]tx 7 — 1 7 —

1 ...

The function F contains both

**nonlinear terms**N, dispersion, dissipation terms Dand Coriolis terms K, F = N + D + K, where for K see (A 1.3) and the main part of

D in small parameters is p1 Pi D = -Ttttt tA^Tu + vo[u utz + (v- uz)uz]tx 7 — 1 7 —

1 ...

Page 77

The weak

can be found by iterating (4.4) over the amplitude, as was done for the density

matrix in Sect. 3.3. To do this, one must change

...

The weak

**nonlinear**dependence of the susceptibility on the electromagnetic fieldcan be found by iterating (4.4) over the amplitude, as was done for the density

matrix in Sect. 3.3. To do this, one must change

**nonlinear**Vlasov**term**/ — ▻ /o +...

Page 131

An estimation of the nonlinear contributions of M in (6.54) in the next order

perturbation theory gives a value that is much less than the

+ wToz. From the expansion in (6.57), taking into account all the approximations,

we ...

An estimation of the nonlinear contributions of M in (6.54) in the next order

perturbation theory gives a value that is much less than the

**nonlinear terms**uTqx+ wToz. From the expansion in (6.57), taking into account all the approximations,

we ...

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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