## Nonlinear Waves in Waveguides: with StratificationS.B. Leble's book deals with nonlinear waves and their propagation in metallic and dielectric waveguides and media with stratification. The underlying nonlinear evolution equations (NEEs) are derived giving also their solutions for specific situations. The reader will find new elements to the traditional approach. Various dispersion and relaxation laws for different guides are considered as well as the explicit form of projection operators, NEEs, quasi-solitons and of Darboux transforms. Special points relate to: 1. the development of a universal asymptotic method of deriving NEEs for guide propagation; 2. applications to the cases of stratified liquids, gases, solids and plasmas with various nonlinearities and dispersion laws; 3. connections between the basic problem and soliton- like solutions of the corresponding NEEs; 4. discussion of details of simple solutions in higher- order nonsingular perturbation theory. |

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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 -(Ttt + 4tf2Da/(7 - 1) - 4(fl, V)[T(«, n) - (fl, V)T] + 2(m

...

After

**scalar**multiplication of (2.24) by fl 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 -(Ttt + 4tf2Da/(7 - 1) - 4(fl, V)[T(«, n) - (fl, V)T] + 2(m

...

Page 24

One can verify that the projection of (2.38) in coordinate representation gives the

system of independent equations W(ta) + iao(-i—)W{a)=0, (2.43) ox where WM =

F*a)$ are the

One can verify that the projection of (2.38) in coordinate representation gives the

system of independent equations W(ta) + iao(-i—)W{a)=0, (2.43) ox where WM =

F*a)$ are the

**scalar**functions (all the components of the equation are ...Page 148

The normalization condition defines the constant r'/2 . . .inh-1 l -1/2 For the

projection by (6.3-5) the

n2z2)-^ (A5.1) EC7V \ 47T2 coShTT-l/^-l)'' _ (Z ,e) = > — — srs = 5. (A5.2) ^

7rsinh7r (1 + ...

The normalization condition defines the constant r'/2 . . .inh-1 l -1/2 For the

projection by (6.3-5) the

**scalar**products are necessary: cosh(1/z0) - (-1)" v2 + (n2z2)-^ (A5.1) EC7V \ 47T2 coShTT-l/^-l)'' _ (Z ,e) = > — — srs = 5. (A5.2) ^

7rsinh7r (1 + ...

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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 frequency 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 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