The rogue waves with quintic nonlinearity and nonlinear dispersion effects in nonlinear optical fibers

Abstract We study on rogue waves in a nonlinear fiber with cubic and quintic nonlinearities, linear and nonlinear dispersion effects. We find the rogue wave with these higher order effects has identical shape with the well-known one in nonlinear Schr o ¨ dinger equation. However, the quintic nonlinear term and nonlinear dispersion effect affect the velocity of rogue wave, and the evolution of its phase.

[1]  R. S. Johnson.  On the modulation of water waves in the neighbourhood of kh ≈ 1.363 , 1977, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[2]  Adrian Ankiewicz,et al.  Solitons : nonlinear pulses and beams , 1997 .

[3]  Janice McMahon,et al.  Rogue Giants at Sea , 2006 .

[4]  Bahram Jalali,et al.  Rogue waves – towards a unifying concept?: Discussions and debates , 2010 .

[5]  C. Garrett.  Rogue waves , 2012 .

[6]  W. Eckhaus,et al.  Nonlinear evolution equations, rescalings, model PDEs and their integrability: II , 1987 .

[7]  Nobuhito Mori,et al.  On Kurtosis and Occurrence Probability of Freak Waves , 2006 .

[8]  V. Zakharov,et al.  On the formation of freak waves on the surface of deep water , 2008 .

[9]  Xianguo Geng,et al.  Darboux Transformation and Soliton Solutions for Generalized Nonlinear Schrödinger Equations , 1999 .

[10]  M Lakshmanan,et al.  Coupled nonlinear Schrödinger equations with cubic-quintic nonlinearity: Integrability and soliton interaction in non-Kerr media. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[11]  About shape of giant breather , 2010 .

[12]  A. Kara,et al.  Solitons, Shock Waves, Conservation Laws and Bifurcation Analysis of Boussinesq Equation with Power Law Nonlinearity and Dual Dispersion , 2014 .

[13]  V. Shrira,et al.  What makes the Peregrine soliton so special as a prototype of freak waves? , 2010 .

[14]  Yuji Kodama,et al.  Optical solitons in a monomode fiber , 1985 .

[15]  B. Jalali,et al.  Optical rogue waves , 2007, Nature.

[16]  Decio Levi,et al.  The Kundu–Eckhaus equation and its discretizations , 2009, 0904.4844.

[17]  C. Finot,et al.  Higher-order modulation instability in nonlinear fiber optics. , 2011, Physical review letters.

[18]  Peter A. Clarkson,et al.  Exact solutions of the multidimensional derivative nonlinear Schrodinger equation for many-body systems of criticality , 1990 .

[19]  Murray Strasberg.  Robert Thomas Beyer , 2009 .

[20]  V. Konotop,et al.  Matter rogue waves , 2009 .

[21]  Frédéric Dias,et al.  The Peregrine soliton in nonlinear fibre optics , 2010 .

[22]  N. Akhmediev,et al.  Waves that appear from nowhere and disappear without a trace , 2009 .

[23]  Adrian Ankiewicz,et al.  Rogue waves and rational solutions of the Hirota equation. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  J. Soto-Crespo,et al.  Extreme waves that appear from nowhere: On the nature of rogue waves , 2009 .

[25]  N. Akhmediev,et al.  The phase patterns of higher-order rogue waves , 2013 .

[26]  Chao-Qing Dai,et al.  Controllable optical rogue waves in the femtosecond regime. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  Anjan Kundu,et al.  Landau-Lifshitz and higher-order nonlinear systems gauge generated from nonlinear Schrödinger-type equations , 1984 .