## Nonlinear waves in waveguides: with stratification |

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Page 12

Traditionally we

We introduce the the mass density of the medium g = m/V where m is the mass in

the volume V. By the vector v we

...

Traditionally we

**denote**by z the vertical and by x, y the horizontal coordinates.We introduce the the mass density of the medium g = m/V where m is the mass in

the volume V. By the vector v we

**denote**the mass velocity with the components v\...

Page 25

... and small amplitudes, W$ + iaii-id/dx)W*> = (/A" - pBn)/(f -Pax), wTM ♢ ioU(-iaia

,w^ - g^ * g • C47) Let the only excited transverse mode be n and let it contain

only one Rossby and one of the Poincare• waves W^K

II, ...

... and small amplitudes, W$ + iaii-id/dx)W*> = (/A" - pBn)/(f -Pax), wTM ♢ ioU(-iaia

,w^ - g^ * g • C47) Let the only excited transverse mode be n and let it contain

only one Rossby and one of the Poincare• waves W^K

**Denote**WTM = R, WTM =II, ...

Page 60

If we

given by the substitution where wsjt = (Ea - Ek)/h. For the matrix gb gbsk = ± exp i

(Wsfc - i/Tsk)t[V, g(0) + g']sk (3.42) holds. The first order perturbation theory ...

If we

**denote**g' = g — gm then the transition of the interaction representation isgiven by the substitution where wsjt = (Ea - Ek)/h. For the matrix gb gbsk = ± exp i

(Wsfc - i/Tsk)t[V, g(0) + g']sk (3.42) holds. The first order perturbation theory ...

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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