## 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 2

Thus, the classic

has given birth to a variety of integrable nonlinear equations – Korteweg–de

Vries (KdV), Kadomtsev–Petviashvili (KP), Nonlinear Schrödinger (NS), ...

Thus, the classic

**waveguide propagation**theory for surface and internal waveshas given birth to a variety of integrable nonlinear equations – Korteweg–de

Vries (KdV), Kadomtsev–Petviashvili (KP), Nonlinear Schrödinger (NS), ...

Page 7

The fundamental statement of the problem has been discussed by Maslov and

Dobrokhotov [1.20–22] as well as in [1.55]. An important case of

dimensions.

The fundamental statement of the problem has been discussed by Maslov and

Dobrokhotov [1.20–22] as well as in [1.55]. An important case of

**waveguide****propagation**is when only one mode is possible due to the waveguidedimensions.

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### Contents

1 | |

Interaction of Modes in an Electromagnetic Field Waveguide | 50 |

Nonlinear Waves in Stratified Plasma | 69 |

Evolution Equations for Internal Waves in Media | 93 |

Mean Field Generation by Waves in a Dissipative Medium | 114 |

Atmospheric Waves over a Rotating Planet 139 | 138 |

Basis Vectors Interaction Operator for Atomic Nuclei | 145 |

Subject Index 161 | 160 |

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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 formulas Fourier frequency given hydrodynamical inhomogeneity initial conditions integration internal waves ion-acoustic ionospheric iteration KdV equation kinetic KP equation Langmuir waves layer linear long waves magnetic field matrix mean field medium method mode interaction mode number nonlinear constants nonlinear terms nonlinear wave nonlocal oscillations perturbation theory physical plasma waves problem projection operators quasi-waveguide quasisolitons region resonance Rossby waves scale Sect small parameters soliton solution spectral 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