# On weakly nonlinear modulation of waves on deep water

@article{Trulsen2000OnWN, title={On weakly nonlinear modulation of waves on deep water}, author={K. Trulsen and I. Kliakhandler and K. Dysthe and M. Velarde}, journal={Physics of Fluids}, year={2000}, volume={12}, pages={2432-2437} }

We propose a new approach for modeling weakly nonlinear waves, based on enhancing truncated amplitude equations with exact linear dispersion. Our example is based on the nonlinear Schrodinger (NLS) equation for deep-water waves. The enhanced NLS equation reproduces exactly the conditions for nonlinear four-wave resonance (the “figure 8” of Phillips) even for bandwidths greater than unity. Sideband instability for uniform Stokes waves is limited to finite bandwidths only, and agrees well with… Expand

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#### References

SHOWING 1-10 OF 18 REFERENCES

A numerical study of water-wave modulation based on a higher-order nonlinear Schrödinger equation

- Physics
- 1985

A modified nonlinear Schrödinger equation for broader bandwidth gravity waves on deep water

- Physics
- 1996

Slow evolution of nonlinear deep water waves in two horizontal directions: A numerical study

- Physics
- 1987

Note on a modification to the nonlinear Schrödinger equation for application to deep water waves

- Mathematics
- Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
- 1979