## 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. |

### From inside the book

Page v

Preface This book emerged from a special course on “

the Kaliningrad State University. An exhaustive overview of research into

Preface This book emerged from a special course on “

**Nonlinear Wave**Theory” atthe Kaliningrad State University. An exhaustive overview of research into

**nonlinear wave**motion in waveguides, in particular, in the USSR, is given. Page 1

1.1 General Remarks In this book the apparatus of the model

equations and the theory of

that result from an inhomogeneity in the propagation medium are presented.

1.1 General Remarks In this book the apparatus of the model

**nonlinear**evolutionequations and the theory of

**wave**interactions in waveguides (quasi-waveguides)that result from an inhomogeneity in the propagation medium are presented.

Page 2

In one-dimensional problems, noticeable progress has been made through the

efforts of many authors [1.12–15], but the essentially multi-dimensional

In one-dimensional problems, noticeable progress has been made through the

efforts of many authors [1.12–15], but the essentially multi-dimensional

**nonlinear****wave**theory is not at all complete. The propagation of waves in guides is one ...Page 26

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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