## Nonlinear waves in waveguides: with stratification |

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Page 17

After

,22). We put (2.22) into (2.23) and differentiate again by t, expressing rot vt by the

transformed (2.24). This gives -(T„ + 4r?2T)«/(7 - 1) - 4(f7, V)[T(«, n) - («, V)T] + ...

After

**scalar**multiplication of (2.24) by (J we differentiate the result by t using (2.21,22). We put (2.22) into (2.23) and differentiate again by t, expressing rot vt by the

transformed (2.24). This gives -(T„ + 4r?2T)«/(7 - 1) - 4(f7, V)[T(«, n) - («, V)T] + ...

Page 24

with stratification Sergeĭ Borisovich Leble. One can verify that the projection of (

2.38) in coordinate representation gives the system of independent equations W$

a) + ioa(-i-^)WM = 0 , (2.43) where W*o) = P(o)d5 are the

...

with stratification Sergeĭ Borisovich Leble. One can verify that the projection of (

2.38) in coordinate representation gives the system of independent equations W$

a) + ioa(-i-^)WM = 0 , (2.43) where W*o) = P(o)d5 are the

**scalar**functions (all the...

Page 96

where w is the solution for the layer [h,H], holds. Equation (5.7) results as the

parts as a result of operating with Lz on the left argument of the

where w is the solution for the layer [h,H], holds. Equation (5.7) results as the

**scalar**product of (5.3) and Zn. The latter term in (5.7) appears after integration byparts as a result of operating with Lz on the left argument of the

**scalar**product.### What people are saying - Write a review

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### Contents

Introduction | 1 |

The Discrimination and Interaction | 12 |

Interaction of Modes in an Electromagnetic Field Waveguide | 50 |

Copyright | |

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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