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
Results 1-5 of 64
Page 3
... Sect . 2.4 and Chap . 4 . The study of interaction of waves with a nonlocal dispersion law is one of the current directions in waveguide propagation theory . It includes the derivation and investigation of BO and Joseph equations as ...
... Sect . 2.4 and Chap . 4 . The study of interaction of waves with a nonlocal dispersion law is one of the current directions in waveguide propagation theory . It includes the derivation and investigation of BO and Joseph equations as ...
Page 4
... ( Sects . 2.5,6 ) . Independent investigations were carried out which showed that in the interaction of two Riemann waves similar results are obtained [ 1.35 ] . The integrability of the CKdV system was studied using the Lax ( Sect . 2.6 ) ...
... ( Sects . 2.5,6 ) . Independent investigations were carried out which showed that in the interaction of two Riemann waves similar results are obtained [ 1.35 ] . The integrability of the CKdV system was studied using the Lax ( Sect . 2.6 ) ...
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... ( Sect . 3.4 ) . Such strong variations in the stratification scale of liquid media lead to nonlocal dispersion of internal waves too . In these cases the waveguide regions appear in a propagation medium where the solutions oscillate and ...
... ( Sect . 3.4 ) . Such strong variations in the stratification scale of liquid media lead to nonlocal dispersion of internal waves too . In these cases the waveguide regions appear in a propagation medium where the solutions oscillate and ...
Page 7
... ( Sects . 2.4,5 ) . The fundamental statement of the problem has been discussed by Maslov and Dobrokhotov [ 1.20-22 ] as ... Sect . 2.5 . The semi - infinite and closed interval solutions for integrable equations may be found in [ 1.66 ] ...
... ( Sects . 2.4,5 ) . The fundamental statement of the problem has been discussed by Maslov and Dobrokhotov [ 1.20-22 ] as ... Sect . 2.5 . The semi - infinite and closed interval solutions for integrable equations may be found in [ 1.66 ] ...
Page 8
... Sect . 2.1 . In addition , the hydrodynamical system of equations is transformed exactly to a system of two equations . This new system is approximately reduced to single equations in Sect . 2.4 and Appendix 1. These equations for ...
... Sect . 2.1 . In addition , the hydrodynamical system of equations is transformed exactly to a system of two equations . This new system is approximately reduced to single equations in Sect . 2.4 and Appendix 1. These equations for ...
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