## Nonlinear waves in waveguides: with stratification |

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Page 23

One can verify that the compatibility condition of (2.37), which is obtained after

the

2.33) with A = — ia. The relationship between the vector components #T = {fl,<p,§

} ...

One can verify that the compatibility condition of (2.37), which is obtained after

the

**substitution**(p = exp(\t)ip, gives the dispersion relation that corresponds to (2.33) with A = — ia. The relationship between the vector components #T = {fl,<p,§

} ...

Page 32

Moreover, the functions 6", after the

(2.65) enter into the integrands and various derivatives so that the right-hand side

looks rather complex. Usually [2.33,43], with the aim of further simplification of ...

Moreover, the functions 6", after the

**substitution**of (2.66) into the nonlinear part of(2.65) enter into the integrands and various derivatives so that the right-hand side

looks rather complex. Usually [2.33,43], with the aim of further simplification of ...

Page 62

(3.51) The last stage of the derivation is the

and of the expressions for the magnetic ... 2.1,2 is convenient and results in

equations of the same type as (3.36) with the

in ...

(3.51) The last stage of the derivation is the

**substitution**of M(2) = JV>(2) into (3.5)and of the expressions for the magnetic ... 2.1,2 is convenient and results in

equations of the same type as (3.36) with the

**substitutions**in the nonlinear termsin ...

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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