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Bonnefoy, F. Haudin, F. Michel, G. Semin, B. Humbert, T. Aumaître, S. Berhanu, M. and Falcon, E. 2016. Observation of resonant interactions among surface gravity waves. Journal of Fluid Mechanics, Vol. 805,
Giannoulis, Ioannis 2016. Interaction of modulated gravity water waves of finite depth. Journal of Differential Equations, Vol. 261, Issue. 7, p. 3864.
Liao, Shijun Xu, Dali and Stiassnie, Michael 2016. On the steady-state nearly resonant waves. Journal of Fluid Mechanics, Vol. 794, p. 175.
Ablowitz, Mark J. and Horikis, Theodoros P. 2015. Interacting nonlinear wave envelopes and rogue wave formation in deep water. Physics of Fluids, Vol. 27, Issue. 1, p. 012107.
Iooss, Gérard 2015. Small Divisor Problems in Fluid Mechanics. Journal of Dynamics and Differential Equations, Vol. 27, Issue. 3-4, p. 787.
Liu, Z. Xu, D. L. Li, J. Peng, T. Alsaedi, A. and Liao, S. J. 2015. On the existence of steady-state resonant waves in experiments. Journal of Fluid Mechanics, Vol. 763, p. 1.
Trulsen, Karsten Nieto Borge, José Carlos Gramstad, Odin Aouf, Lotfi and Lefèvre, Jean-Michel 2015. Crossing sea state and rogue wave probability during the Prestige accident. Journal of Geophysical Research: Oceans, Vol. 120, Issue. 10, p. 7113.
Waseda, Takuji Kinoshita, T. Cavaleri, L. and Toffoli, A. 2015. Third-order resonant wave interactions under the influence of background current fields. Journal of Fluid Mechanics, Vol. 784, p. 51.
She Liam, Lie Adytia, D. and van Groesen, E. 2014. Embedded wave generation for dispersive surface wave models. Ocean Engineering, Vol. 80, p. 73.
Onorato, M. Residori, S. Bortolozzo, U. Montina, A. and Arecchi, F.T. 2013. Rogue waves and their generating mechanisms in different physical contexts. Physics Reports, Vol. 528, Issue. 2, p. 47.
Carter, John D. 2012. Plane-wave solutions of a dissipative generalization of the vector nonlinear Schrödinger equation. Mathematics and Computers in Simulation, Vol. 82, Issue. 6, p. 1038.
Cavaleri, L. Bertotti, L. Torrisi, L. Bitner-Gregersen, E. Serio, M. and Onorato, M. 2012. Rogue waves in crossing seas: The Louis Majesty accident. Journal of Geophysical Research: Oceans, Vol. 117, Issue. C11, p. n/a.
Madsen, Per A. and Fuhrman, David R. 2012. Third-order theory for multi-directional irregular waves. Journal of Fluid Mechanics, Vol. 698, p. 304.
Rabinovitch, A. Biton, Y. Braunstein, D. Friedman, M. and Aviram, I. 2012. Time-periodic lattice of spiral pairs in excitable media. Physical Review E, Vol. 85, Issue. 3,
Iooss, Gérard and Plotnikov, Pavel 2011. Asymmetrical Three-Dimensional Travelling Gravity Waves. Archive for Rational Mechanics and Analysis, Vol. 200, Issue. 3, p. 789.
Islas, A. and Schober, C.M. 2011. Rogue waves, dissipation, and downshifting. Physica D: Nonlinear Phenomena, Vol. 240, Issue. 12, p. 1041.
Deconinck, Bernard and Lovit, David O. 2010. Data analysis and reduction using stationary solutions of the NLS equation. Applicable Analysis, Vol. 89, Issue. 4, p. 611.
HENDERSON, DIANE M. SEGUR, HARVEY and CARTER, JOHN D. 2010. Experimental evidence of stable wave patterns on deep water. Journal of Fluid Mechanics, Vol. 658, p. 247.
Onorato, M. Proment, D. and Toffoli, A. 2010. Freak waves in crossing seas. The European Physical Journal Special Topics, Vol. 185, Issue. 1, p. 45.
Suret, Pierre Randoux, Stéphane Jauslin, Hans R. and Picozzi, Antonio 2010. Anomalous Thermalization of Nonlinear Wave Systems. Physical Review Letters, Vol. 104, Issue. 5,
Experiments are conducted to generate progressive wave fields in deep water with two-dimensional surface patterns for which two parameters are systematically varied: (i) the aspect ratio of the cells comprising the surface patterns and (ii) a measure of nonlinearity of the input wave field. The goal of these experiments is to determine whether these patterns persist, what their main features are, whether standard models of waves describe these features, and whether there are parameter regimes in which the patterns are stable. We find that in some parameter regimes, surface patterns in deep water do persist with little change of form during the time of the experiment. In other parameter regimes, particularly for large-amplitude experiments, the patterns evolve more significantly. We characterize the patterns and their evolutions with a list of observed features. To describe the patterns and features, we consider two models: ($a$) the standard ($2+1$) nonlinear Schrödinger equation and ($b$) coupled nonlinear Schrödinger equations for two interacting wavetrains. Exact solutions of these models provide qualitative explanations for many of the observed features.
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