Management of breather interactions

Gelash, Andrey; Xu, Gang; Kibler, Bertrand

doi:10.1103/physrevresearch.4.033197

Cited by 12 publications

(19 citation statements)

References 63 publications

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“…The corresponding solution exhibits a particular case of type III solution (no degeneration of the solution occurs). (C) Spectral parameter belongs to the Akhmediev region, see Equation (61). The corresponding solution exhibits a particular case of type III Tajiri-Watanabe dynamics (no spatially periodic dynamic occurs).…”

Section: Vector Breathers Of Types I Ii and Iiimentioning

confidence: 99%

“…In addition for the whole range of spectral parameter, 𝑘 I > 𝑘 III , so that 𝑘 I cannot be represent as a sum of 𝑘 II and 𝑘 III . To conclude this section, we consider the particular cases of the resonance interactions corresponding to the choices of the eigenvalues (61)(62)(63). For the eigenvalue of the Kuznetsov type (61), we observe a standing wave group exhibiting complex oscillations, see Figure 8A.…”

Section: Resonance Interactions Of Breathersmentioning

confidence: 99%

“…Then, we analyze solution () at large times, see computational details in Ref. 61, and also in Appendix Section A.3, and find the asymptotic state for each of the breathers. The full asymptotic state of the solution () at

t \rightarrow \pm \infty

represents single breathers with shifted position δ and phase θ parameters, as well as shifted general phase,

\begin{eqnarray} \psi _{1,2}^{\mathrm{I+I}}(\lambda _1,\delta _1,\theta _1;\lambda _2,\delta _2,\theta _2) \rightarrow {\begin{cases} e^{\mp 2\,\mathrm{i}\,s_1 \alpha _2} \psi _{1,2}^\mathrm{I}(\lambda _1,\delta _1 + \delta ^{\pm }_{0,1},\theta _1 + \theta ^{\pm }_{0,1}), \quad \text{at}\quad x\sim V_{\mathrm{I_1}}t, \\ \\ e^{\mp 2\,\mathrm{i}\,s_2 \alpha _1} \psi _{1,2}^\mathrm{I}(\lambda _2,\delta _2 + \delta ^{\pm }_{0,2},\theta _2 + \theta ^{\pm }_{0,2}), \quad \text{at}\quad x\sim V_{\mathrm{I_2}}t, \end{cases}} \end{eqnarray}

where the sign

s_{i} = \pm 1

…”

Section: Elastic Collisions Of Breathersmentioning

confidence: 99%

“…Vector breathers of the type II with spectral parameters defined by Equations(61)(62)(63). (A) Spectral parameter belongs to the Kuznetsov region, see Equation(61). The corresponding solution is a standing dark-bright oscillating breather.…”

mentioning

confidence: 99%

“…(B) Spectral parameter belongs to the Peregrine region, see Equation (61). (C) Spectral parameter belongs to the Akhmediev region, see Equation(61).…”

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Vector breathers in the Manakov system

Gelash

Расковалов

2023

Stud Appl Math

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We study theoretically the nonlinear interactions of vector breathers propagating on an unstable wavefield background. As a model, we use the two‐component extension of the one‐dimensional focusing nonlinear Schrödinger equation—the Manakov system. With the dressing method, we generate the multibreather solutions to the Manakov model. As shown previously in [D. Kraus, G. Biondini, and G. Kovačič, Nonlinearity 28(9), 3101, (2015)], the class of vector breathers is presented by three fundamental types I, II, and III. Their interactions produce a broad family of the two‐component (polarized) nonlinear wave patterns. First, we demonstrate that the type I and the types II and III correspond to two different branches of the dispersion law of the Manakov system in the presence of the unstable background. Then, we investigate the key interaction scenarios, including collisions of standing and moving breathers and resonance breather transformations. Analysis of the two‐breather solution allows us to derive general formulas describing phase and space shifts acquired by breathers in mutual collisions. The found expressions enable us to describe the asymptotic states of the breather interactions and interpret the resonance fusion and decay of breathers as a limiting case of infinite space shift in the case of merging breather eigenvalues. Finally, we demonstrate that only type I breathers participate in the development of modulation instability from small‐amplitude perturbations withing the superregular scenario, while the breathers of types II and III, belonging to the stable branch of the dispersion law, are not involved in this process.

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Section: Vector Breathers Of Types I Ii and Iiimentioning

confidence: 99%

Section: Resonance Interactions Of Breathersmentioning

confidence: 99%

t \rightarrow \pm \infty

represents single breathers with shifted position δ and phase θ parameters, as well as shifted general phase,

\begin{eqnarray} \psi _{1,2}^{\mathrm{I+I}}(\lambda _1,\delta _1,\theta _1;\lambda _2,\delta _2,\theta _2) \rightarrow {\begin{cases} e^{\mp 2\,\mathrm{i}\,s_1 \alpha _2} \psi _{1,2}^\mathrm{I}(\lambda _1,\delta _1 + \delta ^{\pm }_{0,1},\theta _1 + \theta ^{\pm }_{0,1}), \quad \text{at}\quad x\sim V_{\mathrm{I_1}}t, \\ \\ e^{\mp 2\,\mathrm{i}\,s_2 \alpha _1} \psi _{1,2}^\mathrm{I}(\lambda _2,\delta _2 + \delta ^{\pm }_{0,2},\theta _2 + \theta ^{\pm }_{0,2}), \quad \text{at}\quad x\sim V_{\mathrm{I_2}}t, \end{cases}} \end{eqnarray}

where the sign

s_{i} = \pm 1

…”

Section: Elastic Collisions Of Breathersmentioning

confidence: 99%

mentioning

confidence: 99%

“…(B) Spectral parameter belongs to the Peregrine region, see Equation (61). (C) Spectral parameter belongs to the Akhmediev region, see Equation(61).…”

mentioning

confidence: 99%

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