## Nonlinear waves in waveguides: with stratification |

### From inside the book

Results 1-3 of 17

Page 3

The application of

oscillations began with the well-known works of A.Poincare\ N.N.Bogolyubov and

B.G.Galerkin. The generalization of their results was done by Taniuti [1.16-19],

Maslov, ...

The application of

**Fourier**analysis and perturbation theory to nonlinearoscillations began with the well-known works of A.Poincare\ N.N.Bogolyubov and

B.G.Galerkin. The generalization of their results was done by Taniuti [1.16-19],

Maslov, ...

Page 90

(4.68) The solution of the system (4.68) is found in the form of

= / f{u)une-p""7nduj , vn= I g<JJ)unt,-''s"2ndw . (4.69) Here w is an auxiliary

integration variable over the interval Qq of the allowed values ~ kL (Fig. 4.1).

(4.68) The solution of the system (4.68) is found in the form of

**Fourier**integrals uğ= / f{u)une-p""7nduj , vn= I g<JJ)unt,-''s"2ndw . (4.69) Here w is an auxiliary

integration variable over the interval Qq of the allowed values ~ kL (Fig. 4.1).

Page 95

(5.3) Further, let the operator Lz generate a Sturm-Liouville problem after a

u>t), LzZn = \nZn, Z„(0) = 0, (5.4) Z'n(h) = ln(k)Zn(h). (5.5) The condition (5.5)

appears ...

(5.3) Further, let the operator Lz generate a Sturm-Liouville problem after a

**Fourier**transformation which is equivalent to the substitution w ~ Z(z)exp i{ekx —u>t), LzZn = \nZn, Z„(0) = 0, (5.4) Z'n(h) = ln(k)Zn(h). (5.5) The condition (5.5)

appears ...

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

Introduction | 1 |

The Discrimination and Interaction | 12 |

Interaction of Modes in an Electromagnetic Field Waveguide | 50 |

Copyright | |

6 other sections not shown

### Other editions - View all

### Common terms and phrases

allows amplitude approximation atmosphere atmospheric waveguide atmospheric waves basis functions boundary conditions calculation CKdV coefficients components considered contribution coordinate decrease denote density density matrix dependence derivation described determined dielectric dimensionless dispersion branches dispersion equation dispersion relation dissipation distribution function dynamical variables effects evolution equations exponential Fiz.Atm.Okean formulas Fourier given hydrodynamical inhomogeneity initial conditions integration internal waves ion-acoustic ionospheric iteration Kaliningrad KdV equation kinetic Langmuir waves layer linear long waves magnetic field matrix mean field medium method mode interaction mode number Moscow nonlinear constants nonlinear terms Nonlinear Waves nonlocal ocean oscillations perturbation theory physical plasma waves problem projection operators quasi-waveguide quasisolitons region resonance Rossby waves S.B.Leble S.BXeble scale Sect small parameters soliton solution spectral SSSR stationary stratified subspaces substitution taking into account temperature thermoclyne thermoconductivity thermospheric three-wave transformed turbulence two-dimensional values velocity vertical wave interaction wave propagation wave vector waveguide propagation wavelength