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 37
... iteration procedure . At each step of the procedure some model system with small parameters is formed . The solutions of these evolution equations have the property that the coordinate dependence changes increase due to the small terms ...
... iteration procedure . At each step of the procedure some model system with small parameters is formed . The solutions of these evolution equations have the property that the coordinate dependence changes increase due to the small terms ...
Page 38
... iteration in equation ( 2.79 ) be carried out as in ( 2.78 ) and the iterated equation have smooth solu- tions with the condition max | N ( 2 ) ( x , t ) | ≤ 1 at t € [ 0 , t2 ] . Then the estimated results derived from perturbation ...
... iteration in equation ( 2.79 ) be carried out as in ( 2.78 ) and the iterated equation have smooth solu- tions with the condition max | N ( 2 ) ( x , t ) | ≤ 1 at t € [ 0 , t2 ] . Then the estimated results derived from perturbation ...
Page 57
... iteration or if the mode interaction is taken into account . The second iteration gives a cubic nonlinearity and ( 3.31 ) becomes the nonlinear Schrödinger equation ( NS ) . The wave modes interaction yields a resonant contribution ...
... iteration or if the mode interaction is taken into account . The second iteration gives a cubic nonlinearity and ( 3.31 ) becomes the nonlinear Schrödinger equation ( NS ) . The wave modes interaction yields a resonant contribution ...
Contents
Introduction | 1 |
The Discrimination and Interaction | 12 |
3 | 33 |
Copyright | |
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amplitude approximation atmosphere B₁ boundary conditions calculation CKdV coefficients components contribution coordinate denote density density matrix dependence derivation described determined dielectric dimensionless dispersion branches dispersion equation dispersion relation dissipation distribution function dynamical variables effects electromagnetic electron evolution equations frequency given group velocities H₂ hydrodynamical inhomogeneity initial conditions integration internal waves ion-acoustic waves ionospheric iteration KdV equation kinetic Langmuir wave layer linear longitudinal longitudinal waves magnetic field matrix mean field medium method mode interaction nonlinear constants nonlinear terms Nonlinear Waves nonlocal oscillations particles perturbation theory physical plasma waves problem projection operators quasisolitons region resonance Rossby waves S.B.Leble scale Sect small parameters soliton solution spectral SSSR stationary subspaces substitution taking into account temperature thermoclyne thermoconductivity thermospheric three-wave transformed turbulence velocity vertical w₁ wave propagation wave vector waveguide propagation wavelength