## One Citation

## References

SHOWING 1-10 OF 24 REFERENCES

### Nonlinear Modulation of Gravity Waves

- Mathematics, Physics
- 1972

Slow modulation of gravity waves on water layer with uniform depth is investigated by using singular perturbation methods. It is found, to the lowest order of perturbation, that the complicated…

### A high-order nonlinear envelope equation for gravity waves in finite-depth water

- Physics
- 2005

A third-order nonlinear envelope equation is derived for surface waves in finite-depth water by assuming small wave steepness, narrow-band spectrum, and small depth as compared to the modulation…

### On finite amplitude water waves

- PhysicsProceedings of the Indian Academy of Sciences Section C: Engineering Sciences
- 1981

The modulation theory for finite amplitude water waves is developed using the variational technique. It is shown how Levi-Civita’s relation, Starr’s relation and the conservation equations all follow…

### The instabilities of gravity waves of finite amplitude in deep water I. Superharmonics

- PhysicsProceedings of the Royal Society of London. A. Mathematical and Physical Sciences
- 1978

In this paper we embark on a calculation of all the normal-mode perturbations of nonlinear, irrotational gravity waves as a function of the wave steepness. The method is to use as coordinates the…

### Non-linear dispersion of water waves

- PhysicsJournal of Fluid Mechanics
- 1967

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…

### The instabilities of gravity waves of finite amplitude in deep water II. Subharmonics

- PhysicsProceedings of the Royal Society of London. A. Mathematical and Physical Sciences
- 1978

Calculation of the normal-mode perturbation of steep irrotational gravity waves, begun in part I, is here extended to a study of the subharmonic perturbations, namely those having horizontal scales…

### On two-dimensional packets of capillary-gravity waves

- PhysicsJournal of Fluid Mechanics
- 1977

The motion of a two-dimensional packet of capillary–gravity waves on water of finite depth is studied. The evolution of a packet is described by two partial differential equations: the nonlinear…

### The instability of periodic surface gravity waves

- MathematicsJournal of Fluid Mechanics
- 2011

Euler's equations describe the dynamics of gravity waves on the surface of an ideal fluid with arbitrary depth. In this paper, we discuss the stability of periodic travelling wave solutions to the…

### Marginal State of Modulational Instability –Note on Benjamin-Feir Instability–

- Physics, Mathematics
- 1983

This paper deals with the marginal state of modulational instability of a nonlinear wave which is governed by a cubic nonlinear Schrodinger (shortly NS) equation far from the marginal state.…