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
... Nonlinear Wave Theory ” at the Kaliningrad State University . An exhaustive overview of research into nonlinear wave ... terms and the time interval in which the asymptotic ( in the small parameter ) representation of the evolution is ...
... Nonlinear Wave Theory ” at the Kaliningrad State University . An exhaustive overview of research into nonlinear wave ... terms and the time interval in which the asymptotic ( in the small parameter ) representation of the evolution is ...
Page viii
... Nonlinear Terms for Interacting Modes of Poincaré and Rossby Waves at a Rotating Channel Surface 141 Appendix 3 Projection to the Eigen Subspaces for Acoustic and Internal Waves 143 Contents IX Appendix 4 Basis Vectors , Interaction ...
... Nonlinear Terms for Interacting Modes of Poincaré and Rossby Waves at a Rotating Channel Surface 141 Appendix 3 Projection to the Eigen Subspaces for Acoustic and Internal Waves 143 Contents IX Appendix 4 Basis Vectors , Interaction ...
Page 4
... terms and dispersion branches separation , have not been pursued there , however . The simplest evolution equation has been de- rived in [ 1.4 ] for a single mode case . The development of nonlinear evolution equations and progress in ...
... terms and dispersion branches separation , have not been pursued there , however . The simplest evolution equation has been de- rived in [ 1.4 ] for a single mode case . The development of nonlinear evolution equations and progress in ...
Page 5
... nonlinear terms that describe the interaction have been divided into two equal parts . This method is useful but does not allow for generalization . The problem of the discrimination and interaction of waves is solved by the transition ...
... nonlinear terms that describe the interaction have been divided into two equal parts . This method is useful but does not allow for generalization . The problem of the discrimination and interaction of waves is solved by the transition ...
Page 8
... nonlinear and dispersion terms . Detailed expressions are given for interaction constants in the long wave range . It is shown that nonlinear dispersion of long Rossby waves is described by a generalized CKdV equation [ 1.29,30 ] ...
... nonlinear and dispersion terms . Detailed expressions are given for interaction constants in the long wave range . It is shown that nonlinear dispersion of long Rossby waves is described by a generalized CKdV equation [ 1.29,30 ] ...
Contents
1 | |
12 | |
2223 | 19 |
5 | 30 |
6 | 37 |
7 | 45 |
88886 | 62 |
Nonlinear Waves in Stratified Plasma | 69 |
3 | 95 |
Waves in Gases Inhomogeneous in Knudsen Number | 106 |
Mean Field Generation by Waves in a Dissipative Medium | 114 |
5 | 134 |
Nonlinear Terms for Interacting Modes of Poincaré | 141 |
Basis Vectors Interaction Operator for Atomic Nuclei | 145 |
Subject Index 161 | 160 |
4 | 88 |
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Common terms and phrases
allows amplitude approximation atmosphere atmospheric waves B₁ basis functions boundary conditions calculation CKdV coefficients components contribution coordinate denote density density matrix dependence derivation described determined dielectric dimensionless dispersion branches dispersion relation dissipation distribution function dynamical variables effects electromagnetic evolution equations Fiz.Atm.Okean frequency given hydrodynamical inhomogeneity initial conditions integration internal waves ion-acoustic Ionosphere iteration KdV equation kinetic Langmuir Langmuir waves layer linear long waves magnetic field matrix mean field medium method mode interaction Moscow Nauka nonlinear constants nonlinear terms Nonlinear Waves nonlocal oscillations perturbation theory physical plasma waves problem projection operators quasisolitons region resonance Rossby waves S.B.Leble scale Sect small parameters soliton solution spectral subspaces substitution taking into account temperature thermoclyne thermoconductivity thermospheric three-wave transformed turbulence values vector velocity vertical w₁ wave propagation wave vector waveguide propagation wavelength пп