Ch. Mahnke and F. Mitschke, “Possibility of an Akhmediev breather decaying into solitons,” Phys. Rev. A 85, 033808 (2012).

[CrossRef]

Y. Ohta and J. Yang, “General high-order rogue waves and their dynamics in the nonlinear Schrödinger equation,” Proc. R. Soc. A 468, 1716–1740 (2012).

[CrossRef]

U. Bandelow and N. Akhmediev, “Persistence of rogue waves in extended nonlinear Schrödinger equations: integrable Sasa–Satsuma case,” Phys. Lett. A 376, 1558–1561 (2012).

[CrossRef]

P. Gaillard, “Families of quasi-rational solutions of the NLS equation and multi-rogue waves,” J. Phys. A 44, 435204(2011).

[CrossRef]

N. Akhmediev and E. Pelinovsky, eds., Issue on “Rogue waves—towards a unifying concept?” Eur. Phys. J. Special Topics 185, 1–266 (2010).

D. V. Skryabin and A. V. Gorbach, “Looking at a soliton through the prism of optical supercontinuum,” Rev. Mod. Phys. 82, 1287–1299 (2010).

[CrossRef]

G. Genty, C. M. de Sterke, O. Bang, F. Dias, N. Akhmediev, and J. M. Dudley, “Collisions and turbulence in optical rogue wave formation,” Phys. Lett. A 374, 989–996 (2010).

[CrossRef]

J. Bethge, A. Husakou, F. Mitschke, F. Noack, U. Griebner, G. Steinmeyer, and J. Herrmann, “Two-octave supercontinuum generation in a water-filled photonic crystal fiber,” Opt. Express 18, 6230–6240 (2010).

[CrossRef]

J. C. Travers, “High average power supercontinuum sources,” Pramana J. Phys. 75, 769–785 (2010).

[CrossRef]

A. Ankiewicz, J. M. Soto-Crespo, and N. Akhmediev, “Rogue waves and rational solutions of the Hirota equation,” Phys. Rev. E 81, 046602 (2010).

[CrossRef]

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, “The Peregrine soliton in nonlinear fibre optics,” Nat. Phys. 6, 790–795 (2010).

[CrossRef]

A. Ankiewicz, N. Devine, and N. Akhmediev, “Are rogue waves robust against perturbations?” Phys. Lett. A 373, 3997–4000 (2009).

[CrossRef]

A. Mussot and A. Kudlinski, “19.5 W CW-pumped supercontinuum source from 0.65 to 1.38 μm,” Electron. Lett. 45, 29–30 (2009).

[CrossRef]

J. M. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, “Modulation instability, Akhmediev breathers and continuous wave supercontinuum generation,” Opt. Express 17, 21497–21508 (2009).

[CrossRef]

A. Mussot, A. Kudlinski, M. Kolobov, E. Louvergneaux, M. Douay, and M. Taki, “Observation of extreme temporal events in CW-pumped supercontinuum,” Opt. Express 17, 17010–17015 (2009).

[CrossRef]

N. Akhmediev, A. Ankiewicz, and M. Taki, “Waves that appear from nowhere and disappear without a trace,” Phys. Lett. A 373, 675–678 (2009).

[CrossRef]

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054–1057 (2007).

[CrossRef]

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).

[CrossRef]

T. Brugarino and M. Sciacca, “Singularity analysis and integrability for a HNLS equation governing pulse propagation in a generic fiber optics,” Opt. Commun. 262, 250–256 (2006).

[CrossRef]

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, “Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett. 88, 173901 (2002).

[CrossRef]

A. V. Husakou and J. Herrmann, “Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers,” Phys. Rev. Lett. 87, 203901 (2001).

[CrossRef]

J. K. Ranka, R. S. Windeler, and A. J. Stentz, “Visible continuum generation in air–silica microstructure optical fiber with anomalous dispersion at 800 nm,” Opt. Lett. 25, 25–27 (2000).

[CrossRef]

Z. Li, L. Li, H. Tian, and G. Zhou, “New types of solitary wave solutions for the higher order nonlinear Schrödinger equation,” Phys. Rev. Lett. 84, 4096–4099 (2000).

[CrossRef]

S. Palacios, A. Guinea, J. M. Fernandez-Diaz, and R. D. Crespo, “Dark solitary waves in the nonlinear Schrödinger equation with third order dispersion, self-steepening, and self-frequency shift,” Phys. Rev. E 60, R45–R47 (1999).

[CrossRef]

S. B. Cavalcanti, J. C. Cressoni, Heber R. da Cruz, and A. S. Gouveia-Neto, “Modulation instability in the region of minimum group-velocity dispersion of single-mode optical fibers via an extended nonlinear Schrödinger equation,” Phys. Rev. A 43, 6162–6165 (1991).

[CrossRef]

N. Sasa and J. Satsuma, “New type of soliton solutions for a higher-order nonlinear Schrödinger equation,” J. Phys. Soc. Jpn. 60, 409–417 (1991).

[CrossRef]

N. Akhmediev, V. I. Korneev, and N. V. Mitskevich, “Modulation instability of CW signal in an optical fiber with the 3rd-order dispersion,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 33, 95–100 (1990); Radiofiz 33, 111–117 (1990).

D. H. Peregrine, “Water waves, nonlinear Schrödinger equations and their solutions,” J. Aust. Math. Soc. B 25, 16–43 (1983).

[CrossRef]

D. Anderson and M. Lisak, “Nonlinear asymmetric self-phase modulation and self-steepening of pulses in long optical waveguides,” Phys. Rev. A 27, 1393–1398 (1983).

[CrossRef]

A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142–144 (1973).

[CrossRef]

R. Hirota, “Exact envelope-soliton solutions of a nonlinear wave equation,” J. Math. Phys. 14, 805–809 (1973).

[CrossRef]

G. P. Agrawal, Nonlinear Fiber Optics, 4th ed., Optics and Photonics series (Academic, 2006), Section 5.5.3.

U. Bandelow and N. Akhmediev, “Persistence of rogue waves in extended nonlinear Schrödinger equations: integrable Sasa–Satsuma case,” Phys. Lett. A 376, 1558–1561 (2012).

[CrossRef]

A. Ankiewicz, J. M. Soto-Crespo, and N. Akhmediev, “Rogue waves and rational solutions of the Hirota equation,” Phys. Rev. E 81, 046602 (2010).

[CrossRef]

G. Genty, C. M. de Sterke, O. Bang, F. Dias, N. Akhmediev, and J. M. Dudley, “Collisions and turbulence in optical rogue wave formation,” Phys. Lett. A 374, 989–996 (2010).

[CrossRef]

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, “The Peregrine soliton in nonlinear fibre optics,” Nat. Phys. 6, 790–795 (2010).

[CrossRef]

J. M. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, “Modulation instability, Akhmediev breathers and continuous wave supercontinuum generation,” Opt. Express 17, 21497–21508 (2009).

[CrossRef]

A. Ankiewicz, N. Devine, and N. Akhmediev, “Are rogue waves robust against perturbations?” Phys. Lett. A 373, 3997–4000 (2009).

[CrossRef]

N. Akhmediev, A. Ankiewicz, and M. Taki, “Waves that appear from nowhere and disappear without a trace,” Phys. Lett. A 373, 675–678 (2009).

[CrossRef]

N. Akhmediev, V. I. Korneev, and N. V. Mitskevich, “Modulation instability of CW signal in an optical fiber with the 3rd-order dispersion,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 33, 95–100 (1990); Radiofiz 33, 111–117 (1990).

N. Akhmediev and A. Ankiewicz, Solitons, Nonlinear Pulses and Beams (Chapman and Hall, 1997).

D. Anderson and M. Lisak, “Nonlinear asymmetric self-phase modulation and self-steepening of pulses in long optical waveguides,” Phys. Rev. A 27, 1393–1398 (1983).

[CrossRef]

A. Ankiewicz, J. M. Soto-Crespo, and N. Akhmediev, “Rogue waves and rational solutions of the Hirota equation,” Phys. Rev. E 81, 046602 (2010).

[CrossRef]

A. Ankiewicz, N. Devine, and N. Akhmediev, “Are rogue waves robust against perturbations?” Phys. Lett. A 373, 3997–4000 (2009).

[CrossRef]

N. Akhmediev, A. Ankiewicz, and M. Taki, “Waves that appear from nowhere and disappear without a trace,” Phys. Lett. A 373, 675–678 (2009).

[CrossRef]

N. Akhmediev and A. Ankiewicz, Solitons, Nonlinear Pulses and Beams (Chapman and Hall, 1997).

U. Bandelow and N. Akhmediev, “Persistence of rogue waves in extended nonlinear Schrödinger equations: integrable Sasa–Satsuma case,” Phys. Lett. A 376, 1558–1561 (2012).

[CrossRef]

G. Genty, C. M. de Sterke, O. Bang, F. Dias, N. Akhmediev, and J. M. Dudley, “Collisions and turbulence in optical rogue wave formation,” Phys. Lett. A 374, 989–996 (2010).

[CrossRef]

T. Brugarino and M. Sciacca, “Singularity analysis and integrability for a HNLS equation governing pulse propagation in a generic fiber optics,” Opt. Commun. 262, 250–256 (2006).

[CrossRef]

S. B. Cavalcanti, J. C. Cressoni, Heber R. da Cruz, and A. S. Gouveia-Neto, “Modulation instability in the region of minimum group-velocity dispersion of single-mode optical fibers via an extended nonlinear Schrödinger equation,” Phys. Rev. A 43, 6162–6165 (1991).

[CrossRef]

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).

[CrossRef]

S. Palacios, A. Guinea, J. M. Fernandez-Diaz, and R. D. Crespo, “Dark solitary waves in the nonlinear Schrödinger equation with third order dispersion, self-steepening, and self-frequency shift,” Phys. Rev. E 60, R45–R47 (1999).

[CrossRef]

S. B. Cavalcanti, J. C. Cressoni, Heber R. da Cruz, and A. S. Gouveia-Neto, “Modulation instability in the region of minimum group-velocity dispersion of single-mode optical fibers via an extended nonlinear Schrödinger equation,” Phys. Rev. A 43, 6162–6165 (1991).

[CrossRef]

S. B. Cavalcanti, J. C. Cressoni, Heber R. da Cruz, and A. S. Gouveia-Neto, “Modulation instability in the region of minimum group-velocity dispersion of single-mode optical fibers via an extended nonlinear Schrödinger equation,” Phys. Rev. A 43, 6162–6165 (1991).

[CrossRef]

G. Genty, C. M. de Sterke, O. Bang, F. Dias, N. Akhmediev, and J. M. Dudley, “Collisions and turbulence in optical rogue wave formation,” Phys. Lett. A 374, 989–996 (2010).

[CrossRef]

A. Ankiewicz, N. Devine, and N. Akhmediev, “Are rogue waves robust against perturbations?” Phys. Lett. A 373, 3997–4000 (2009).

[CrossRef]

G. Genty, C. M. de Sterke, O. Bang, F. Dias, N. Akhmediev, and J. M. Dudley, “Collisions and turbulence in optical rogue wave formation,” Phys. Lett. A 374, 989–996 (2010).

[CrossRef]

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, “The Peregrine soliton in nonlinear fibre optics,” Nat. Phys. 6, 790–795 (2010).

[CrossRef]

J. M. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, “Modulation instability, Akhmediev breathers and continuous wave supercontinuum generation,” Opt. Express 17, 21497–21508 (2009).

[CrossRef]

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, “The Peregrine soliton in nonlinear fibre optics,” Nat. Phys. 6, 790–795 (2010).

[CrossRef]

G. Genty, C. M. de Sterke, O. Bang, F. Dias, N. Akhmediev, and J. M. Dudley, “Collisions and turbulence in optical rogue wave formation,” Phys. Lett. A 374, 989–996 (2010).

[CrossRef]

J. M. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, “Modulation instability, Akhmediev breathers and continuous wave supercontinuum generation,” Opt. Express 17, 21497–21508 (2009).

[CrossRef]

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).

[CrossRef]

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, “The Peregrine soliton in nonlinear fibre optics,” Nat. Phys. 6, 790–795 (2010).

[CrossRef]

S. Palacios, A. Guinea, J. M. Fernandez-Diaz, and R. D. Crespo, “Dark solitary waves in the nonlinear Schrödinger equation with third order dispersion, self-steepening, and self-frequency shift,” Phys. Rev. E 60, R45–R47 (1999).

[CrossRef]

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, “The Peregrine soliton in nonlinear fibre optics,” Nat. Phys. 6, 790–795 (2010).

[CrossRef]

P. Gaillard, “Families of quasi-rational solutions of the NLS equation and multi-rogue waves,” J. Phys. A 44, 435204(2011).

[CrossRef]

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, “The Peregrine soliton in nonlinear fibre optics,” Nat. Phys. 6, 790–795 (2010).

[CrossRef]

G. Genty, C. M. de Sterke, O. Bang, F. Dias, N. Akhmediev, and J. M. Dudley, “Collisions and turbulence in optical rogue wave formation,” Phys. Lett. A 374, 989–996 (2010).

[CrossRef]

J. M. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, “Modulation instability, Akhmediev breathers and continuous wave supercontinuum generation,” Opt. Express 17, 21497–21508 (2009).

[CrossRef]

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).

[CrossRef]

D. V. Skryabin and A. V. Gorbach, “Looking at a soliton through the prism of optical supercontinuum,” Rev. Mod. Phys. 82, 1287–1299 (2010).

[CrossRef]

S. B. Cavalcanti, J. C. Cressoni, Heber R. da Cruz, and A. S. Gouveia-Neto, “Modulation instability in the region of minimum group-velocity dispersion of single-mode optical fibers via an extended nonlinear Schrödinger equation,” Phys. Rev. A 43, 6162–6165 (1991).

[CrossRef]

J. Bethge, A. Husakou, F. Mitschke, F. Noack, U. Griebner, G. Steinmeyer, and J. Herrmann, “Two-octave supercontinuum generation in a water-filled photonic crystal fiber,” Opt. Express 18, 6230–6240 (2010).

[CrossRef]

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, “Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett. 88, 173901 (2002).

[CrossRef]

S. Palacios, A. Guinea, J. M. Fernandez-Diaz, and R. D. Crespo, “Dark solitary waves in the nonlinear Schrödinger equation with third order dispersion, self-steepening, and self-frequency shift,” Phys. Rev. E 60, R45–R47 (1999).

[CrossRef]

A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142–144 (1973).

[CrossRef]

J. Bethge, A. Husakou, F. Mitschke, F. Noack, U. Griebner, G. Steinmeyer, and J. Herrmann, “Two-octave supercontinuum generation in a water-filled photonic crystal fiber,” Opt. Express 18, 6230–6240 (2010).

[CrossRef]

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, “Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett. 88, 173901 (2002).

[CrossRef]

A. V. Husakou and J. Herrmann, “Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers,” Phys. Rev. Lett. 87, 203901 (2001).

[CrossRef]

R. Hirota, “Exact envelope-soliton solutions of a nonlinear wave equation,” J. Math. Phys. 14, 805–809 (1973).

[CrossRef]

J. Bethge, A. Husakou, F. Mitschke, F. Noack, U. Griebner, G. Steinmeyer, and J. Herrmann, “Two-octave supercontinuum generation in a water-filled photonic crystal fiber,” Opt. Express 18, 6230–6240 (2010).

[CrossRef]

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, “Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett. 88, 173901 (2002).

[CrossRef]

A. V. Husakou and J. Herrmann, “Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers,” Phys. Rev. Lett. 87, 203901 (2001).

[CrossRef]

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054–1057 (2007).

[CrossRef]

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, “The Peregrine soliton in nonlinear fibre optics,” Nat. Phys. 6, 790–795 (2010).

[CrossRef]

J. M. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, “Modulation instability, Akhmediev breathers and continuous wave supercontinuum generation,” Opt. Express 17, 21497–21508 (2009).

[CrossRef]

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, “Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett. 88, 173901 (2002).

[CrossRef]

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054–1057 (2007).

[CrossRef]

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, “Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett. 88, 173901 (2002).

[CrossRef]

N. Akhmediev, V. I. Korneev, and N. V. Mitskevich, “Modulation instability of CW signal in an optical fiber with the 3rd-order dispersion,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 33, 95–100 (1990); Radiofiz 33, 111–117 (1990).

A. Mussot, A. Kudlinski, M. Kolobov, E. Louvergneaux, M. Douay, and M. Taki, “Observation of extreme temporal events in CW-pumped supercontinuum,” Opt. Express 17, 17010–17015 (2009).

[CrossRef]

A. Mussot and A. Kudlinski, “19.5 W CW-pumped supercontinuum source from 0.65 to 1.38 μm,” Electron. Lett. 45, 29–30 (2009).

[CrossRef]

Z. Li, L. Li, H. Tian, and G. Zhou, “New types of solitary wave solutions for the higher order nonlinear Schrödinger equation,” Phys. Rev. Lett. 84, 4096–4099 (2000).

[CrossRef]

Z. Li, L. Li, H. Tian, and G. Zhou, “New types of solitary wave solutions for the higher order nonlinear Schrödinger equation,” Phys. Rev. Lett. 84, 4096–4099 (2000).

[CrossRef]

D. Anderson and M. Lisak, “Nonlinear asymmetric self-phase modulation and self-steepening of pulses in long optical waveguides,” Phys. Rev. A 27, 1393–1398 (1983).

[CrossRef]

Ch. Mahnke and F. Mitschke, “Possibility of an Akhmediev breather decaying into solitons,” Phys. Rev. A 85, 033808 (2012).

[CrossRef]

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, “The Peregrine soliton in nonlinear fibre optics,” Nat. Phys. 6, 790–795 (2010).

[CrossRef]

Ch. Mahnke and F. Mitschke, “Possibility of an Akhmediev breather decaying into solitons,” Phys. Rev. A 85, 033808 (2012).

[CrossRef]

J. Bethge, A. Husakou, F. Mitschke, F. Noack, U. Griebner, G. Steinmeyer, and J. Herrmann, “Two-octave supercontinuum generation in a water-filled photonic crystal fiber,” Opt. Express 18, 6230–6240 (2010).

[CrossRef]

N. Akhmediev, V. I. Korneev, and N. V. Mitskevich, “Modulation instability of CW signal in an optical fiber with the 3rd-order dispersion,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 33, 95–100 (1990); Radiofiz 33, 111–117 (1990).

A. Mussot, A. Kudlinski, M. Kolobov, E. Louvergneaux, M. Douay, and M. Taki, “Observation of extreme temporal events in CW-pumped supercontinuum,” Opt. Express 17, 17010–17015 (2009).

[CrossRef]

A. Mussot and A. Kudlinski, “19.5 W CW-pumped supercontinuum source from 0.65 to 1.38 μm,” Electron. Lett. 45, 29–30 (2009).

[CrossRef]

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, “Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett. 88, 173901 (2002).

[CrossRef]

Y. Ohta and J. Yang, “General high-order rogue waves and their dynamics in the nonlinear Schrödinger equation,” Proc. R. Soc. A 468, 1716–1740 (2012).

[CrossRef]

S. Palacios, A. Guinea, J. M. Fernandez-Diaz, and R. D. Crespo, “Dark solitary waves in the nonlinear Schrödinger equation with third order dispersion, self-steepening, and self-frequency shift,” Phys. Rev. E 60, R45–R47 (1999).

[CrossRef]

D. H. Peregrine, “Water waves, nonlinear Schrödinger equations and their solutions,” J. Aust. Math. Soc. B 25, 16–43 (1983).

[CrossRef]

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054–1057 (2007).

[CrossRef]

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, “Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett. 88, 173901 (2002).

[CrossRef]

N. Sasa and J. Satsuma, “New type of soliton solutions for a higher-order nonlinear Schrödinger equation,” J. Phys. Soc. Jpn. 60, 409–417 (1991).

[CrossRef]

N. Sasa and J. Satsuma, “New type of soliton solutions for a higher-order nonlinear Schrödinger equation,” J. Phys. Soc. Jpn. 60, 409–417 (1991).

[CrossRef]

T. Brugarino and M. Sciacca, “Singularity analysis and integrability for a HNLS equation governing pulse propagation in a generic fiber optics,” Opt. Commun. 262, 250–256 (2006).

[CrossRef]

D. V. Skryabin and A. V. Gorbach, “Looking at a soliton through the prism of optical supercontinuum,” Rev. Mod. Phys. 82, 1287–1299 (2010).

[CrossRef]

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054–1057 (2007).

[CrossRef]

A. Ankiewicz, J. M. Soto-Crespo, and N. Akhmediev, “Rogue waves and rational solutions of the Hirota equation,” Phys. Rev. E 81, 046602 (2010).

[CrossRef]

A. Mussot, A. Kudlinski, M. Kolobov, E. Louvergneaux, M. Douay, and M. Taki, “Observation of extreme temporal events in CW-pumped supercontinuum,” Opt. Express 17, 17010–17015 (2009).

[CrossRef]

N. Akhmediev, A. Ankiewicz, and M. Taki, “Waves that appear from nowhere and disappear without a trace,” Phys. Lett. A 373, 675–678 (2009).

[CrossRef]

A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142–144 (1973).

[CrossRef]

Z. Li, L. Li, H. Tian, and G. Zhou, “New types of solitary wave solutions for the higher order nonlinear Schrödinger equation,” Phys. Rev. Lett. 84, 4096–4099 (2000).

[CrossRef]

J. C. Travers, “High average power supercontinuum sources,” Pramana J. Phys. 75, 769–785 (2010).

[CrossRef]

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, “Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett. 88, 173901 (2002).

[CrossRef]

Y. Ohta and J. Yang, “General high-order rogue waves and their dynamics in the nonlinear Schrödinger equation,” Proc. R. Soc. A 468, 1716–1740 (2012).

[CrossRef]

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, “Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett. 88, 173901 (2002).

[CrossRef]

Z. Li, L. Li, H. Tian, and G. Zhou, “New types of solitary wave solutions for the higher order nonlinear Schrödinger equation,” Phys. Rev. Lett. 84, 4096–4099 (2000).

[CrossRef]

A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142–144 (1973).

[CrossRef]

A. Mussot and A. Kudlinski, “19.5 W CW-pumped supercontinuum source from 0.65 to 1.38 μm,” Electron. Lett. 45, 29–30 (2009).

[CrossRef]

N. Akhmediev and E. Pelinovsky, eds., Issue on “Rogue waves—towards a unifying concept?” Eur. Phys. J. Special Topics 185, 1–266 (2010).

N. Akhmediev, V. I. Korneev, and N. V. Mitskevich, “Modulation instability of CW signal in an optical fiber with the 3rd-order dispersion,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 33, 95–100 (1990); Radiofiz 33, 111–117 (1990).

D. H. Peregrine, “Water waves, nonlinear Schrödinger equations and their solutions,” J. Aust. Math. Soc. B 25, 16–43 (1983).

[CrossRef]

R. Hirota, “Exact envelope-soliton solutions of a nonlinear wave equation,” J. Math. Phys. 14, 805–809 (1973).

[CrossRef]

P. Gaillard, “Families of quasi-rational solutions of the NLS equation and multi-rogue waves,” J. Phys. A 44, 435204(2011).

[CrossRef]

N. Sasa and J. Satsuma, “New type of soliton solutions for a higher-order nonlinear Schrödinger equation,” J. Phys. Soc. Jpn. 60, 409–417 (1991).

[CrossRef]

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, “The Peregrine soliton in nonlinear fibre optics,” Nat. Phys. 6, 790–795 (2010).

[CrossRef]

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054–1057 (2007).

[CrossRef]

T. Brugarino and M. Sciacca, “Singularity analysis and integrability for a HNLS equation governing pulse propagation in a generic fiber optics,” Opt. Commun. 262, 250–256 (2006).

[CrossRef]

A. Mussot, A. Kudlinski, M. Kolobov, E. Louvergneaux, M. Douay, and M. Taki, “Observation of extreme temporal events in CW-pumped supercontinuum,” Opt. Express 17, 17010–17015 (2009).

[CrossRef]

J. M. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, “Modulation instability, Akhmediev breathers and continuous wave supercontinuum generation,” Opt. Express 17, 21497–21508 (2009).

[CrossRef]

J. Bethge, A. Husakou, F. Mitschke, F. Noack, U. Griebner, G. Steinmeyer, and J. Herrmann, “Two-octave supercontinuum generation in a water-filled photonic crystal fiber,” Opt. Express 18, 6230–6240 (2010).

[CrossRef]

U. Bandelow and N. Akhmediev, “Persistence of rogue waves in extended nonlinear Schrödinger equations: integrable Sasa–Satsuma case,” Phys. Lett. A 376, 1558–1561 (2012).

[CrossRef]

N. Akhmediev, A. Ankiewicz, and M. Taki, “Waves that appear from nowhere and disappear without a trace,” Phys. Lett. A 373, 675–678 (2009).

[CrossRef]

G. Genty, C. M. de Sterke, O. Bang, F. Dias, N. Akhmediev, and J. M. Dudley, “Collisions and turbulence in optical rogue wave formation,” Phys. Lett. A 374, 989–996 (2010).

[CrossRef]

A. Ankiewicz, N. Devine, and N. Akhmediev, “Are rogue waves robust against perturbations?” Phys. Lett. A 373, 3997–4000 (2009).

[CrossRef]

Ch. Mahnke and F. Mitschke, “Possibility of an Akhmediev breather decaying into solitons,” Phys. Rev. A 85, 033808 (2012).

[CrossRef]

D. Anderson and M. Lisak, “Nonlinear asymmetric self-phase modulation and self-steepening of pulses in long optical waveguides,” Phys. Rev. A 27, 1393–1398 (1983).

[CrossRef]

S. B. Cavalcanti, J. C. Cressoni, Heber R. da Cruz, and A. S. Gouveia-Neto, “Modulation instability in the region of minimum group-velocity dispersion of single-mode optical fibers via an extended nonlinear Schrödinger equation,” Phys. Rev. A 43, 6162–6165 (1991).

[CrossRef]

S. Palacios, A. Guinea, J. M. Fernandez-Diaz, and R. D. Crespo, “Dark solitary waves in the nonlinear Schrödinger equation with third order dispersion, self-steepening, and self-frequency shift,” Phys. Rev. E 60, R45–R47 (1999).

[CrossRef]

A. Ankiewicz, J. M. Soto-Crespo, and N. Akhmediev, “Rogue waves and rational solutions of the Hirota equation,” Phys. Rev. E 81, 046602 (2010).

[CrossRef]

Z. Li, L. Li, H. Tian, and G. Zhou, “New types of solitary wave solutions for the higher order nonlinear Schrödinger equation,” Phys. Rev. Lett. 84, 4096–4099 (2000).

[CrossRef]

A. V. Husakou and J. Herrmann, “Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers,” Phys. Rev. Lett. 87, 203901 (2001).

[CrossRef]

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, “Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett. 88, 173901 (2002).

[CrossRef]

J. C. Travers, “High average power supercontinuum sources,” Pramana J. Phys. 75, 769–785 (2010).

[CrossRef]

Y. Ohta and J. Yang, “General high-order rogue waves and their dynamics in the nonlinear Schrödinger equation,” Proc. R. Soc. A 468, 1716–1740 (2012).

[CrossRef]

D. V. Skryabin and A. V. Gorbach, “Looking at a soliton through the prism of optical supercontinuum,” Rev. Mod. Phys. 82, 1287–1299 (2010).

[CrossRef]

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).

[CrossRef]

J. M. Dudley and J. R. Taylor, eds., Supercontinuum Generation in Optical Fibers (Cambridge University, 2010).

N. Akhmediev and A. Ankiewicz, Solitons, Nonlinear Pulses and Beams (Chapman and Hall, 1997).

G. P. Agrawal, Nonlinear Fiber Optics, 4th ed., Optics and Photonics series (Academic, 2006), Section 5.5.3.