Possibility of an Akhmediev breather decaying into solitons

Mahnke, Christoph; Mitschke, F.

doi:10.1103/physreva.85.033808

Cited by 66 publications

(51 citation statements)

References 34 publications

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“…We can fix one of the eigenvalues, say λ 2 , and find the other one, λ 1 , using equation (4.1). For each λ 2 , we obtain a curve on the complex plane for λ 1 . The results are presented in figure 4.…”

Section: Higher Order Breather Superpositionsmentioning

confidence: 99%

“…Acting the same way as before, we fix the eigenvalue λ 2 and find the eigenvalues λ 1 that satisfy the condition of equation (6.1). Now, equation (6.1) can be solved analytically for b 1 . We find that b 1 = ± √ p 1 /p 2 , where figure 9a.…”

Section: Superposition Of Moving Breathers Of the Nonlinear Schrödingmentioning

confidence: 99%

“…Breathers can be converted into solitons with special perturbations [1]. Solitons themselves can evolve into the form of breathers [2].…”

Section: Introductionmentioning

confidence: 99%

“…One of the simplest equations of this type is the so-called Hirota equation (HE) [4,5]. 1 2 [6], but this is not essential. The choice of η = 1 2 only becomes important when we want to keep circular symmetry of rogue wave clusters in the (x, t)-plane [7,8].…”

Section: Introductionmentioning

confidence: 99%

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Moving breathers and breather-to-soliton conversions for the Hirota equation

Chowdury¹,

Ankiewicz²,

Akhmediev³

2015

Proc. R. Soc. A.

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We find that the Hirota equation admits breather-tosoliton conversion at special values of the solution eigenvalues. This occurs for the first-order, as well as higher orders, of breather solutions. An analytic expression for the condition of the transformation is given and several examples of transformations are presented. The values of these special eigenvalues depend on two free parameters that are present in the Hirota equation. We also find that higher order breathers generally have complicated quasi-periodic oscillations along the direction of propagation. Various breather solutions are considered, including the particular case of second-order breathers of the nonlinear Schrödinger equation.

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Section: Higher Order Breather Superpositionsmentioning

confidence: 99%

Section: Superposition Of Moving Breathers Of the Nonlinear Schrödingmentioning

confidence: 99%

“…Breathers can be converted into solitons with special perturbations [1]. Solitons themselves can evolve into the form of breathers [2].…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Moving breathers and breather-to-soliton conversions for the Hirota equation

Chowdury¹,

Ankiewicz²,

Akhmediev³

2015

Proc. R. Soc. A.

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“…In particular, soliton solutions are robust and their propagation is not hampered by the presence of perturbations [29]. Moreover, Mahnke and Mitschke [41] have shown that the Akhmediev breather solutions of the NLSE are also robust. They cannot be destroyed by small perturbations of the solution.…”

Section: Robustness Of Periodic Orbitsmentioning

confidence: 98%

Adiabatic transformation of continuous waves into trains of pulses

2017

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Periodic structures may grow in both conservative and dissipative systems. A multiplicity of examples can be found in nature and in the laboratory. However, periodic structures may grow and decay. We show that the effects of dissipation are essential for these structures to remain. Using the nonlinear Schrödinger equation and its extensions as basic examples of conservative and dissipative systems we show that there are two ways of adiabatic transformations of a continuous-wave solution into a train of pulses.

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Predictability horizon of oceanic rogue waves

Alam

2014

Geophysical Research Letters

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Prediction is a central goal and a yet-unresolved challenge in the investigation of oceanic rogue waves. Here we define a horizon of predictability for oceanic rogue waves and derive, via extensive computational experiments, a statistically converged predictability time scale for these structures. We show that this time scale is a function of the sea state (i.e., severity of the ambient ocean waves), the height of the anticipated rogue wave, and the level of uncertainties in the ocean measurements. The presented predictability time scale establishes a quantitative metric on the combined temporal effects of the variety of mechanisms that together lead to the formation of a rogue wave and is crucial for the assessment of validity of rogue wave predictions, as well as for the critical evaluation of results from the widely used model equations.

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Possibility of an Akhmediev breather decaying into solitons

Cited by 66 publications

References 34 publications

Moving breathers and breather-to-soliton conversions for the Hirota equation

Moving breathers and breather-to-soliton conversions for the Hirota equation

Adiabatic transformation of continuous waves into trains of pulses

Predictability horizon of oceanic rogue waves

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