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 35
... solution , at sufficiently long time , will not have any physical sense . The correct solution can be found as a piecewise regular function , as is the case in shock wave theory [ 2.68 ] . For the piecewise smooth generalized solutions ...
... solution , at sufficiently long time , will not have any physical sense . The correct solution can be found as a piecewise regular function , as is the case in shock wave theory [ 2.68 ] . For the piecewise smooth generalized solutions ...
Page 38
... solution of On + cnon2 + oNn ( 1 ) ( 8 ) = o2 Ñn ( 2 ) + ... .. differs from the solution of the equation with a zero right - hand side by a value that does not exceed σ . In Sect . 2.6 we consider an example of such a second iteration ...
... solution of On + cnon2 + oNn ( 1 ) ( 8 ) = o2 Ñn ( 2 ) + ... .. differs from the solution of the equation with a zero right - hand side by a value that does not exceed σ . In Sect . 2.6 we consider an example of such a second iteration ...
Page 39
... solutions for CKdV . However , in this case in ( 2.84 ) the mode velocity difference cn - cm must replace c . Thus the solutions must be stable . In contrast to the approach of [ 2.72 ] we suggest finding a solution not as a row , but ...
... solutions for CKdV . However , in this case in ( 2.84 ) the mode velocity difference cn - cm must replace c . Thus the solutions must be stable . In contrast to the approach of [ 2.72 ] we suggest finding a solution not as a row , but ...
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