Long-time dynamics of the modulational instability of deep water waves

  title={Long-time dynamics of the modulational instability of deep water waves},
  author={Mark J. Ablowitz and Julie Hammack and Douglas Henderson and Constance M. Schober},
In this paper, we experimentally and theoretically examine the long-time evolution of modulated periodic 1D Stokes waves which are described, to leading-order, by the nonlinear Schrödinger (NLS) equation. The laboratory and numerical experiments indicate that under suitable conditions modulated periodic wave trains evolve chaotically. A Floquet spectral decomposition of the laboratory data at sampled times shows that the waveform exhibits bifurcations across standing wave states to leftand… CONTINUE READING


Publications referenced by this paper.
Showing 1-10 of 15 references


G. G. Stokes
Trans. 8 • 1847
View 12 Excerpts
Highly Influenced


Y. Li, D. W. McLaughlin, J. Shatah, S. Wiggins
Pure Appl. Math. 49 • 1996
View 2 Excerpts


A. Calini
Ercolani, D.W. McLaughlin, C.M. Schober, Physica D 89 • 1996
View 1 Excerpt


D. W. McLaughlin, E. A. Overman
Appl. Math. 1 • 1995


M. J. Ablowitz, C. M. Schober
Math. 172 • 1994
View 1 Excerpt

Its, V.B. Matveev, Algebro-geometric Approach to Nonlinear Integrable Problems, Springer Series in Nonlinear Dynamics

E. D. Belokolos, A. I. Bobenko, A.R.V.Z. Enol’skii
View 1 Excerpt


M. G. Forest, C. G. Goedde
Sinha, Physica D 67 • 1993
View 1 Excerpt


E. Lo, C. C. Mei
Fluid Mech. 150 • 1985
View 1 Excerpt

Solitons and the Inverse Scattering Transform

M. J. Ablowitz, H. Segur
SIAM, Philadelphia, PA • 1981
View 1 Excerpt


K. B. Dysthe
Roy. Soc. London A 369 • 1979
View 1 Excerpt

Similar Papers

Loading similar papers…