Circular rogue wave clusters

Kedziora, David J.; Ankiewicz, Adrian; Akhmediev, Nail

doi:10.1103/physreve.84.056611

Cited by 216 publications

(254 citation statements)

References 26 publications

(51 reference statements)

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“…The richer family of multirogue wave solutions of the NLSE is also very attractive for future works. These more general higher-order solutions exhibit multiple maxima, i.e., multiple rogue waves, with a complex spatiotemporal arrangement [27,[33][34][35][36].…”

Section: Discussionmentioning

confidence: 99%

Collision of Akhmediev Breathers in Nonlinear Fiber Optics

2013

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We report here a novel fiber-based test bed using tailored spectral shaping of an optical-frequency comb to excite the formation of two Akhmediev breathers that collide during propagation. We have found specific initial conditions by controlling the phase and velocity differences between breathers that lead, with certainty, to their efficient collision and the appearance of a giant-amplitude wave. Temporal and spectral characteristics of the collision dynamics are in agreement with the corresponding analytical solution. We anticipate that experimental evidence of breather-collision dynamics is of fundamental importance in the understanding of extreme ocean waves and in other disciplines driven by the continuous nonlinear Schrödinger equation.

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Section: Discussionmentioning

confidence: 99%

Collision of Akhmediev Breathers in Nonlinear Fiber Optics

2013

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“…et al, study the order N ¼ 2 in [32], N ¼ 3 in [33]; the case N ¼ 4 was studied in particular (N ¼ 5; 6 were also studied) in [34,35] showing triangle and arc patterns; only one type of ring was presented. The extrapolation was done until the order N ¼ 9 in [36].…”

Section: Resultsmentioning

confidence: 99%

Patterns of deformations of Peregrine breather of order 3 and 4 solutions to the NLS equation with multi parameters

Gaillard

2016

J Theor Appl Phys

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In this article, one gives a classification of the solutions to the one dimensional nonlinear focusing Schrödinger equation (NLS) by considering the modulus of the solutions in the (x, t) plan in the cases of orders 3 and 4. For this, we use a representation of solutions to NLS equation as a quotient of two determinants by an exponential depending on t. This formulation gives in the case of the order 3 and 4, solutions with, respectively 4 and 6 parameters. With this method, beside Peregrine breathers, we construct all characteristic patterns for the modulus of solutions, like triangular configurations, ring and others.

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“…From the figures, we find that the maximum height of the k-th order rogue wave is (2k + 1) 2 . As remarked in [31,32], there are…”

Section: Solutions From Periodic Solutionmentioning

confidence: 90%