Orbital Instability of the Peregrine Soliton
Abbreviated Journal Title
J. Phys. Soc. Jpn.
ROGUE WAVES; SUPERCONTINUUM GENERATION; MODULATION INSTABILITY; SCHRODINGER-EQUATIONS; FREAK WAVE; DEEP-WATER; DYNAMICS; FIBER; MECHANISMS; STABILITY; Physics, Multidisciplinary
The Peregrine soliton is one possible model of a rogue wave. Importantly, this type of soliton corresponds nicely to rogue waves recently observed experimentally in a water tank [A. Chabchoub, N. P. Hoffmann, and N. Akhmediev, Phys. Rev. Lett. 106, 204502 (2011)] and in optical fiber [B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, Nat. Phys. 6, 790 (2010)]. Starting with a family of Peregrine solitons indexed by their spectral parameter, we analytically demonstrate a type of instability in the Peregrine soliton through a concise orbital stability analysis. This analysis is completely analytical, and to verify the approach we also discuss a numerical linear instability analysis. We give the growth/decay rate for these solitons as a function of the initial amplitude, which for each soliton shall depend on the spectral parameter.
Journal of the Physical Society of Japan
"Orbital Instability of the Peregrine Soliton" (2014). Faculty Bibliography 2010s. 6213.