Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/american-physical-society-aps/super-rogue-waves-in-simulations-based-on-weakly-nonlinear-and-fully-Wrh0P04xBk
References (59)
-
A. Chabchoub, N. Hoffmann, N. Akhmediev (2011)
Rogue wave observation in a water wave tank.Physical review letters, 106 20
-
P. Gaillard (2012)
WRONSKIAN REPRESENTATION OF SOLUTIONS OF THE NLS EQUATION AND HIGHER PEREGRINE BREATHERS -
(1979)
Proc. Roy. Soc. London A -
(2012)
Abstracts of the IUTAM Symposium Waves in Fluids: Effects of Non-linearity, Rotation, Stratification and Dissipation -
(2008)
Annu. Rev. Fluid. Mech -
K. Dysthe (1979)
Note on a modification to the nonlinear Schrödinger equation for application to deep water wavesProceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 369
-
M. Onorato, A. Osborne, M. Serio, S. Bertone (2001)
Freak waves in random oceanic sea states.Physical review letters, 86 25
-
(2001)
Phys. Rev. Lett -
(2012)
Simulations and experiments of Euler solitons in surface water waves. Under revision for -
N. Shelkovnikov (2014)
Rogue waves in the oceanBulletin of the Russian Academy of Sciences: Physics, 78
-
(2006)
Eur. J. Mech. B -
N. Akhmediev, A. Ankiewicz, M. Taki (2009)
Waves that appear from nowhere and disappear without a tracePhysics Letters A, 373
-
E. Krause (1981)
Advances in fluid mechanics: proceedings of a conference held at Aachen, March 26-28, 1980 -
V. Zakharov, A. Shabat (1970)
Exact Theory of Two-dimensional Self-focusing and One-dimensional Self-modulation of Waves in Nonlinear MediaJournal of Experimental and Theoretical Physics, 34
-
(1971)
Eksp. Teor. Fiz.Sov. Phys. JETP -
(2012)
A. Slunyaev and V. Shrira, On the highest non-breaking wave in a group: fully nonlinear water wave breathers vs weakly nonlinear theory -
Kharif Christian, Slunyaev Alexey, Pelinovsky Efim (2009)
Rogue Waves in the Ocean -
V. Zakharov, A. Dyachenko, O. Vasilyev (2002)
New method for numerical simulation of a nonstationary potential flow of incompressible fluid with a free surfaceEuropean Journal of Mechanics B-fluids, 21
-
J. Engelbrecht (2015)
What is wave motion -
E. Kuznetsov (1977)
Solitons in a parametrically unstable plasma, 236
-
P. Dubard, Pierre Gaillard, Christian Klein, Vladimir Matveev (2010)
On multi-rogue wave solutions of the NLS equation and positon solutions of the KdV equationThe European Physical Journal Special Topics, 185
-
(1987)
Gener - ation of periodic trains of picosecond pulses in an optical fiber : exact solutions -
(1987)
Theor. Math. Phys. USSR 72 -
(1977)
Doklady USSR 236 -
A. Slunyaev, I. Didenkulova, E. Pelinovsky (2011)
Rogue watersContemporary Physics, 52
-
A. Chabchoub, N. Hoffmann, M. Onorato, A. Slunyaev, A. Sergeeva, E. Pelinovsky, N. Akhmediev (2012)
Observation of a hierarchy of up to fifth-order rogue waves in a water tank.Physical review. E, Statistical, nonlinear, and soft matter physics, 86 5 Pt 2
-
(2006)
in Waves in Geophysical Fluids: Tsunamis -
(1985)
Sov. Phys. JETP 62 -
M. Onorato, A. Osborne, M. Serio, L. Cavaleri, C. Brandini, C. Stansberg (2006)
Extreme waves, modulational instability and second order theory: wave flume experiments on irregular wavesEuropean Journal of Mechanics B-fluids, 25
-
A. Chabchoub, N. Akhmediev, N. Hoffmann (2012)
Experimental study of spatiotemporally localized surface gravity water waves.Physical review. E, Statistical, nonlinear, and soft matter physics, 86 1 Pt 2
-
D. Peregrine (1983)
Water waves, nonlinear Schrödinger equations and their solutionsThe Journal of the Australian Mathematical Society. Series B. Applied Mathematics, 25
-
A. Chabchoub, N. Hoffmann, M. Onorato, N. Akhmediev (2012)
Super Rogue Waves: Observation of a Higher-Order Breather in Water WavesPhysical Review X, 2
-
and as an in -
F. Fedele (2015)
On Oceanic Rogue WavesarXiv: Atmospheric and Oceanic Physics
-
K. Trulsen (2006)
Weakly nonlinear and stochastic properties of ocean wave fields. Application to an extreme wave event -
N. Akhmediev, A. Ankiewicz, J. Soto-Crespo (2009)
Rogue waves and rational solutions of the nonlinear Schrödinger equation.Physical review. E, Statistical, nonlinear, and soft matter physics, 80 2 Pt 2
-
A. Osborne (2010)
Nonlinear Ocean Waves and the Inverse Scattering Transform -
(2010)
J. Eng. Math -
J. Grue, K. Trulsen (2006)
Waves in geophysical fluids : tsunamis, rogue waves, internal waves and internal tides -
(2012)
J. Math. Sci.: Adv. Appl -
N. Akhmediev, V. Eleonskii, N. Kulagin (1987)
Exact first-order solutions of the nonlinear Schrödinger equationTheoretical and Mathematical Physics, 72
-
B. West, K. Brueckner, R. Janda, D. Milder, R. Milton (1987)
A new numerical method for surface hydrodynamicsJournal of Geophysical Research, 92
-
(2009)
Teor. Fiz -
(1996)
A modified nonlinear Schrdinger equation for broader bandwidth gravity waves on deep water -
(2011)
Contemp -
(1995)
Physical Review E -
(2013)
Phys. Fluids -
A. Slunyaev (2005)
A high-order nonlinear envelope equation for gravity waves in finite-depth waterJournal of Experimental and Theoretical Physics, 101
-
H. Arakawa (1932)
On Water WavesJournal of the Meteorological Society of Japan, 10
-
(1983)
Austral. Math. Soc. Ser. B -
(1987)
J. Geophys. Res -
Mitsuhiro Tanaka (1990)
Maximum amplitude of modulated wavetrainWave Motion, 12
-
V. Zakharov (1968)
Stability of periodic waves of finite amplitude on the surface of a deep fluidJournal of Applied Mechanics and Technical Physics, 9
-
(1968)
Appl. Mech. Tech. Phys.Zh. Prikl. Mekh. Fiz -
(2010)
Eur. Phys. J. Special Topics -
E. Krause, Y. Fung (1982)
Advances in Fluid Mechanics -
V. Shrira, V. Geogjaev (2010)
What makes the Peregrine soliton so special as a prototype of freak waves?Journal of Engineering Mathematics, 67
-
A. Slunyaev (2009)
Numerical simulation of “limiting” envelope solitons of gravity waves on deep waterJournal of Experimental and Theoretical Physics, 109
-
L. Shemer, A. Sergeeva, A. Slunyaev (2010)
Applicability of envelope model equations for simulation of narrow-spectrum unidirectional random wave field evolution: Experimental validationPhysics of Fluids, 22
- Publisher
- American Physical Society (APS)
- Copyright
- ©2013 American Physical Society
- ISSN
- 1539-3755
- DOI
- 10.1103/PhysRevE.88.012909
- pmid
- 23944540
- Publisher site
- See Article on Publisher Site
Abstract
The rogue wave solutions (rational multibreathers) of the nonlinear Schrödinger equation (NLS) are tested in numerical simulations of weakly nonlinear and fully nonlinear hydrodynamic equations. Only the lowest order solutions from 1 to 5 are considered. A higher accuracy of wave propagation in space is reached using the modified NLS equation, also known as the Dysthe equation. This numerical modeling allowed us to directly compare simulations with recent results of laboratory measurements in Chabchoub ( Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.86.056601 86 , 056601 ( 2012 ) ). In order to achieve even higher physical accuracy, we employed fully nonlinear simulations of potential Euler equations. These simulations provided us with basic characteristics of long time evolution of rational solutions of the NLS equation in the case of near-breaking conditions. The analytic NLS solutions are found to describe the actual wave dynamics of steep waves reasonably well.
Journal
Physical Review E – American Physical Society (APS)
Published: Jul 19, 2013