Group velocity and nonlinear dispersive wave propagation

@article{Hayes1973GroupVA,
  title={Group velocity and nonlinear dispersive wave propagation},
  author={Wallace Dean Hayes},
  journal={Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences},
  year={1973},
  volume={332},
  pages={199 - 221}
}
  • W. Hayes
  • Published 6 March 1973
  • Physics
  • Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
By the use of a Hamiltonian formulation, a basic group velocity is defined as the derivative of frequency with respect to wavenumber keeping action density constant, and is shown to represent an incremental action velocity in the general nonlinear case. The stability treatment of Whitham and Lighthill is extended to several dimensions. The water-wave analysis of Whitham (1967 a) is extended to two space dimensions, and is shown to predict oblique-mode instabilities for kh < 1.36. A treatment of… 
Dispersive phi4 wave propagation
Whitham's theory (1965) of nonlinear water waves is applied to a nonlinear c-number field ( lambda phi 4 model) to investigate the propagation characteristics of the field in the plane-wave modes. A
Exact solutions of a three-dimensional nonlinear Schrödinger equation applied to gravity waves
The three-dimensional evolution of packets of gravity waves is studied using a nonlinear Schrödinger equation (the Davey–Stewartson equation). It is shown that permanent wave groups of the elliptic
Nonlinear chiral dispersive waves
Whitham's theory of nonlinear water waves is applied to a classical field with the lagrangian density L=1/2((( delta mu phi )( delta mu phi )-m2 phi 2)/(1+ lambda phi 2)). This is the isoscalar
Effect of dissipation and dispersion on slowly varying wavetrains
A kinematic model for disturbance wave motions slowly modulated in space and time is developed, which describes the effects of amplitude and frequency dispersion, modal dependence, flow
A note on the Lagrangian method for nonlinear dispersive waves
This paper makes a few remarks on the method of the averaged Lagrangian developed by Whitham to describe slow variations of nonlinear wave trains. The concept of multiple scales is incorporated into
Material space and dual canonical wave formulation : Application to nonlinear elastic solids
It is shown that the kinematic wave theory develops in parallel with the "materials mechanics" but in terms of frequency and material wave vector instead of time and material coordinates. A
On three-dimensional packets of surface waves
  • A. Davey, K. Stewartson
  • Physics
    Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
  • 1974
In this note we use the method of multiple scales to derive the two coupled nonlinear partial differential equations which describe the evolution of a three-dimensional wave-packet of wavenumber k on
Addition of dispersive terms to the method of averaged Lagrangian
Whitham's method of averaged Lagrangian is applied to the problem of Stokes waves on the surface of a layer of ideal fluid. We derive a Lagrangian which contains additional terms with ax2 and aaxx
Derivative-Expansion Method for Nonlinear Waves on a Liquid Layer of Slowly Varying Depth
An extended form of the derivative-expansion method is applied to the study of nonlinear capillary-gravity waves on a liquid layer of slowly varying depth. Generalized expressions of the nonlinear
...
1
2
3
4
5
...

References

SHOWING 1-7 OF 7 REFERENCES
A general approach to linear and non-linear dispersive waves using a Lagrangian
The basic property of equations describing dispersive waves is the existence of solutions representing uniform wave trains. In this paper a general theory is given for non-uniform wave trains whose
Kinematic wave theory
  • W. Hayes
  • Physics
    Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
  • 1970
In the kinematic theory of wave propagation (e. g. geometrical optics) a quantity J is needed in the calculation of wave intensity either through transport equations or the principle of conservation
Conservation of action and modal wave action
  • W. Hayes
  • Physics
    Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
  • 1970
For a system governed by a Lagrangian density a local action density and flux are defined for a family of solutions periodic in a parameter, and this action obeys an absolute conservation law. In the
Non-linear dispersion of water waves
The slow dispersion of non-linear water waves is studied by the general theory developed in an earlier paper (Whitham 1965b). The average Lagrangian is calculated from the Stokes expansion for
Variational methods and applications to water waves
  • G. Whitham
  • Mathematics
    Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
  • 1967
This paper reviews various uses of variational methods in the theory of nonlinear dispersive waves, with details presented for water waves. The appropriate variational principle for water waves is
Non-linear dispersive waves
  • G. Whitham
  • Mathematics
    Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
  • 1965
A general theory is developed for studying changes of a wave train governed by non-linear partial differential equations. The technique is to average over the local oscillations in the medium and so
Two-timing, variational principles and waves
In this paper, it is shown how the author's general theory of slowly varying wave trains may be derived as the first term in a formal perturbation expansion. In its most effective form, the