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 1
... integration of the model evolution equations . The success of the theory includes the development of experimental soliton physics and the investigation of organized nonlinear phenomena . Examples are investigations of surface and ...
... integration of the model evolution equations . The success of the theory includes the development of experimental soliton physics and the investigation of organized nonlinear phenomena . Examples are investigations of surface and ...
Page 3
... integration was developed . This allows one to reduce the wave disturbance solution , which is nearly a single - mode wave , to the solution of a combined KdV - MKdV equation [ 1.33 ] ( by the same amplitude parameter as in the ...
... integration was developed . This allows one to reduce the wave disturbance solution , which is nearly a single - mode wave , to the solution of a combined KdV - MKdV equation [ 1.33 ] ( by the same amplitude parameter as in the ...
Page 7
... integration was developed for nonlocal dispersion in [ 1.54 ] . The soliton solutions of single mode evolution equations are generally a rather crude approximation in waveguide theory . However , they can be the starting point for the ...
... integration was developed for nonlocal dispersion in [ 1.54 ] . The soliton solutions of single mode evolution equations are generally a rather crude approximation in waveguide theory . However , they can be the starting point for the ...
Page 10
... integration of the discrete Silin - Tikhonchuk equations is given . These describe the interaction of antiparallel Langmuir waves [ 1.75 ] . The equations are a new example of an integrable system and contain solitons with new ...
... integration of the discrete Silin - Tikhonchuk equations is given . These describe the interaction of antiparallel Langmuir waves [ 1.75 ] . The equations are a new example of an integrable system and contain solitons with new ...
Page 23
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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