Numerical study of the generation and evolution of breather-type rogue waves

References

• Akhmediev N, Ankiewicz A, Soto-Crespo JM. 2009. Rogue waves and rational solutions of the nonlinear Schrödinger equation. Phys Rev E Stat Nonlinear Soft Matter Phys. 80(2):026601–026609.
   Web of Science ®Google Scholar
• Akhmediev N, Ankiewicz A, Taki M. 2009. Waves that appear from nowhere and disappear without a trace. Phys Lett Sect A Gen At Solid State Phys. 373(6):675–678.
   Google Scholar
• Akhmediev N, Eleonskii V, Kulagin N. 1985. Generation of periodic trains of picosecond pulses in an optical fiber: exact solutions. Sov Phys JETP. 62(5):894–899.
   Google Scholar
• Akhmediev N, Eleonskii V, Kulagin N. 1987. Exact first-order solutions of the nonlinear Schrödinger equation. TheoMath Phys. 72(2):809–818.
   Web of Science ®Google Scholar
• Chabchoub A, Hoffmann NP, Akhmediev N. 2011. Rogue wave observation in a water wave tank. Phys Rev Lett. 106(20):309–313.
   Web of Science ®Google Scholar
• Chereskin TK, Mollo-Christensen E. 1985. Modulational development of nonlinear gravity-wave groups. J Fluid Mech. 151:337–365.
   Web of Science ®Google Scholar
• Deng Y, Yang J, Tian X, Li X. 2015. Experimental investigation on rogue waves and their impacts on a vertical cylinder using the Peregrine breather model. Ships Offshore Struct. 1–9.
   Web of Science ®Google Scholar
• Dubard P, Gaillard P, Klein C, Matveev VB. 2010. On multi-rogue wave solutions of the NLS equation and positon solutions of the KdV equation.Eur Phys J Spec Top. 185(1):247–258.
   Web of Science ®Google Scholar
• Dysthe KB. 1979. Note on a modification to the nonlinear Schrodinger equation for application to deep water waves. Proc R Soc Lond A Math Phys Sci. 369(1736):105–114.
   Web of Science ®Google Scholar
• Gaillard P. 2012. Wronskian representation of solutions of the NLS equation and higher Peregrine breathers. Sci Adv. 13(2):71–153.
   Google Scholar
• Haver S. 2003. Freak wave event at Draupner jacket Januar 1 1995.
   Google Scholar
• Kit E, Shemer L. 2002. Spatial versions of the Zakharov and Dysthe evolution equations for deep-water gravity waves. J Fluid Mech. 450:201–205.
   Web of Science ®Google Scholar
• Lake BM, Yuen HC, Rungaldier H, Ferguson WE. 1977. Nonlinear deep-water waves: theory and experiment – 2. Evolution of a continuous wave train. J Fluid Mech. 83(pt 1):49–74.
   Web of Science ®Google Scholar
• Liu PC, MacHutchon KR. 2008. Are there different kinds of rogue waves? J. Offshore Mech Arc. 130(2):822–830.
   Web of Science ®Google Scholar
• Lo E, Mei CC. 1985. Numerical study of water-wave modulation based on a higher-order nonlinear schrodinger equation. J Fluid Mech. 150:395–416.
   Web of Science ®Google Scholar
• Ma YC. 1979. Perturbed plane-wave solutions of the cubic schrodinger equation. Stud Appl Math. 60(1):43–58.
   Web of Science ®Google Scholar
• Mei CC. 1989. The applied dynamics of ocean surface waves. Singapore: World Scientific.
   Google Scholar
• Melville WK. 1982. The instability and breaking of deep-water waves. J Fluid Mech. 115(Feb):165–185.
   Web of Science ®Google Scholar
• Mori N, Liu PC, Yasuda T. 2002. Analysis of freak wave measurements in the Sea of Japan. Ocean Eng. 29(11):1399–1414.
   Web of Science ®Google Scholar
• Onorato M, Osborne AR, Serio M, Bertone S. 2001. Freak waves in random oceanic sea states. Phys Rev Lett. 86(25):5831–5834.
   PubMed Web of Science ®Google Scholar
• Onorato M, Osborne AR, Serio M, Cavaleri L, Brandini C, Stansberg CT. 2006. Extreme waves, modulational instability and second order theory: wave flume experiments on irregular waves. Eur J Mech B/Fluids. 25(5):586–601.
   Web of Science ®Google Scholar
• Pelinovsky E, Slunyaev A, Lopatoukhin L, Divinsky B, Levin B. 2004. Freak Wave event in the Black Sea: observation and modeling. Dokl Earth Sci A. 395:438–443.
   Google Scholar
• Peregrine D. 1983. Water waves, nonlinear Schrödinger equations and their solutions. J Aust Math Soc B. 25(1):16–43.
   Google Scholar
• Shemer L, Alperovich L. 2013. Peregrine breather revisited. Phys Fluids. 25(5):157–164.
   Web of Science ®Google Scholar
• Shemer L, Kit E, Jiao H. 2002. An experimental and numerical study of the spatial evolution of unidirectional nonlinear water-wave groups. Phys Fluids. 14(10):3380–3390.
   Web of Science ®Google Scholar
• Shemer L, Kit E, Jiao H, Eitan O. 1998. Experiments on nonlinear wave groups in intermediate water depth. J Waterw Port Coast Ocean Eng. 124(6):320–327.
   Web of Science ®Google Scholar
• Shemer L, Sergeeva A, Slunyaev A. 2010. Applicability of envelope model equations for simulation of narrow-spectrum unidirectional random wave field evolution: Experimental validation. Phys Fluids. 22(1):1–9.
   Web of Science ®Google Scholar
• Shrira VI, Geogjaev VV. 2010. What makes the Peregrine soliton so special as a prototype of freak waves? J Eng Math. 67(1):11–22.
   Web of Science ®Google Scholar
• Stiassnie M. 1984. Note on the modified nonlinear Schrödinger equation for deep water waves. Wave Mot. 6(4):431–433.
   Web of Science ®Google Scholar
• Torrence C, Compo GP. 1998. A Practical Guide to Wavelet Analysis. Bull Am Meteorol Soc. 79(1):61–78.
   Web of Science ®Google Scholar
• Trulsen K, Dysthe KB. 1996. A modified nonlinear Schrödinger equation for broader bandwidth gravity waves on deep water. Wave Mot. 24(3):281–289.
   Web of Science ®Google Scholar
• Trulsen K, Stansberg CT. 2001. Spatial evolution of water surface waves: numerical simulation and experiment of bichromatic waves. Proceedings of the 11th (2001) International Offshore and Polar Engineering Conference; 2001 Jun 17–22; Stavanger, Norway.
   Google Scholar
• Yuen HC, Lake BM. 1982. Nonlinear dynamics of deep-water gravity waves. Adv Appl Mech. 22(82):67–229.
   Web of Science ®Google Scholar
• Zakharov VE. 1968. Stability of periodic waves of finite amplitude on the surface of a deep fluid. J Appl Mech Tech Phys. 9(2):190–194.
   Google Scholar