Optimal self-compression of multisoliton pulses in an optical fiber

Akhmediev, NN; Betina, L. L.; Eleonskiǐ, V. M.; Kulagin, N. E.; Ostrovskaya, N. V.; Poltoratskiĭ, É. A.

doi:10.1070/qe1989v019n09abeh009130

Cited by 59 publications

(90 citation statements)

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“…(1) reduces to the standard NLS equation (2). Several localized and periodic structures of standard NLS are documented in the literature [21,46,47]. Equation (2) admits N th order RW solution.…”

Section: Appendix Amentioning

confidence: 99%

“…To begin with we consider the first-order breather solution of the NLS equation (2), which is given in [46] and is a special case of the GB solution (4), where the parameters f and v are expressed in terms of a complex eigenvalue (say λ), that is f = 2 √ 1 + λ 2 and v = Im(λ), and X 1 and T 1 serve as coordinate shifts from the origin. The real part of the eigenvalue represents the angle that the one-dimensionally localized solutions form with the T axis, and the imaginary part characterizes frequency of periodic modulation.…”

Section: Characteristics Of Breathersmentioning

confidence: 99%

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Manipulating matter rogue waves and breathers in Bose-Einstein condensates

et al. 2014

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We construct higher order rogue wave solutions and breather profiles for the quasi-one-dimensional Gross-Pitaevskii equation with a time-dependent interatomic interaction and external trap through the similarity transformation technique. We consider three different forms of traps, namely (i) timeindependent expulsive trap, (ii) time-dependent monotonous trap and (iii) time-dependent periodic trap. Our results show that when we change a parameter appearing in the time-independent or time-dependent trap the second and third-order rogue waves transform into the first-order like rogue waves. We also analyze the density profiles of breather solutions. Here also we show that the shapes of the breathers change when we tune the strength of trap parameter. Our results may help to manage rogue waves experimentally in a BEC system.

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Section: Appendix Amentioning

confidence: 99%

Section: Characteristics Of Breathersmentioning

confidence: 99%

Manipulating matter rogue waves and breathers in Bose-Einstein condensates

et al. 2014

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“…(6) cannot be found analytically, but it is possible to find them numerically. 12,14 Analytically we can find only the points of bifurcation at which these states split off from the polarized ones.…”

Section: (10)mentioning

confidence: 99%

“…The phases of the two components are locked in the following composite (nonpolarized) solitonstate solutions 12,13 …”

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confidence: 99%

Phase-locked stationary soliton states in birefringent nonlinear optical fibers

Akhmediev

Buryak

Soto-Crespo³

et al. 1995

J. Opt. Soc. Am. B

114

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We consider stationary soliton states in a birefringent optical fiber with two components locked in phase. Two values of the phase difference between the two components of the soliton states are studied: 0 and p͞2. These cases allow us to find composite soliton states in a simple way. The bifurcation diagrams for the coupled soliton states in these two cases are constructed. The stability of these soliton states is examined also.Propagation of soliton pulses in birefringent nonlinear fibers has been studied intensively in recent years.

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“…In this model the discrete spectrum solutions, interacting with condensate, transform from solitons to the oscillating structures -breathers. The family of NLSE breathers includes the well known solutions of Pere-grine [12], Kuznetsov-Ma [10,11] and Akhmediev [13].…”

Section: Introductionmentioning

confidence: 99%

Formation of rogue waves from a locally perturbed condensate

Gelash

2018

Phys. Rev. E

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The one-dimensional focusing nonlinear Schrödinger equation (NLSE) on an unstable condensate background is the fundamental physical model, that can be applied to study the development of modulation instability (MI) and formation of rogue waves. The complete integrability of the NLSE via inverse scattering transform enables the decomposition of the initial conditions into elementary nonlinear modes: breathers and continuous spectrum waves. The small localized condensate perturbations (SLCP) that grow as a result of MI have been of fundamental interest in nonlinear physics for many years. Here, we demonstrate that Kuznetsov-Ma and superregular NLSE breathers play the key role in the dynamics of a wide class of SLCP. During the nonlinear stage of MI development, collisions of these breathers lead to the formation of rogue waves. We present new scenarios of rogue wave formation for randomly distributed breathers as well as for artificially prepared initial conditions. For the latter case, we present an analytical description based on the exact expressions found for the space-phase shifts that breathers acquire after collisions with each other. Finally, the presence of Kuznetsov-Ma and superregular breathers in arbitrary-type condensate perturbations is demonstrated by solving the Zakharov-Shabat eigenvalue problem with high numerical accuracy.

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Optimal self-compression of multisoliton pulses in an optical fiber

Cited by 59 publications

References 0 publications

Manipulating matter rogue waves and breathers in Bose-Einstein condensates

Manipulating matter rogue waves and breathers in Bose-Einstein condensates

Phase-locked stationary soliton states in birefringent nonlinear optical fibers

Formation of rogue waves from a locally perturbed condensate

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