Breathers, solitons and rogue waves of the quintic nonlinear Schrödinger equation on various backgrounds

Nikolić, Stanko N.; Ashour, Omar A.; Aleksić, Najdan B.; Belić, Milivoj R.; Chin, Siu A.

doi:10.1007/s11071-018-4726-8

Cited by 25 publications

(25 citation statements)

References 37 publications

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“…The discussion here leans a lot on the results obtained in [53]. We choose the dn function as the background [7,8,53]:…”

Section: Talbot Carpets For the Hirota And Hirota-quintic Equationmentioning

confidence: 99%

“…with φ = 1 2 (2 − m) c 2 + γ c 4 6 − 6m + m 2 and v = (2 − m) αc 3 + δc 5 6 − 6m + m 2 . Next, we calculate an arbitrary-order breather on the elliptic background, using the procedure described in detail in [53].…”

Section: Talbot Carpets For the Hirota And Hirota-quintic Equationmentioning

confidence: 99%

“…As shown in Sect. 5 of [53], the matching of the higher-order breather period T B to the period of the dn background T dn may lead to the appearance of periodic RWs. This means that the ratio of periods q = T B /T dn should be a positive integer.…”

Section: Talbot Carpets For the Hirota And Hirota-quintic Equationmentioning

confidence: 99%

“…We take c = 1, α = − 0.03, γ = − 0.0614, and δ = 0.7. We use expressions from [53] to calculate m = 0.1192, ν 1 = 0.92, and ν 2 = 0.83, leading to q = 9 and T B2 = T B1 /2. Here, ν 1 and ν 2 are the eigenvalues of the first two unstable modes, according to the DT.…”

Section: Talbot Carpets For the Hirota And Hirota-quintic Equationmentioning

confidence: 99%

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Talbot carpets by rogue waves of extended nonlinear Schrödinger equations

et al. 2019

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We present analytical and numerical doubleperiodic solutions of the one-dimensional nonlinear Schrödinger equation and its extended versions in the form of Talbot carpets. The breathers and rogue waves of different orders are obtained using numerical simulations, starting from the initial conditions calculated by the Darboux transformation. To suppress undesirable aspects of modulation instability leading to homoclinic chaos, Fourier mode pruning procedures are invented to preserve and maintain the twofold periodicity of carpets. The novelty of this paper is analytical Talbot carpets for Hirota-quintic equation and ability to obtain them dynamically by controlling the growth of the Fourier modes. In addition, the new period-matching procedure is also described for periodic rogue waves that can be utilized to produce Talbot carpets without

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“…The discussion here leans a lot on the results obtained in [53]. We choose the dn function as the background [7,8,53]:…”

Section: Talbot Carpets For the Hirota And Hirota-quintic Equationmentioning

confidence: 99%

Section: Talbot Carpets For the Hirota And Hirota-quintic Equationmentioning

confidence: 99%

Section: Talbot Carpets For the Hirota And Hirota-quintic Equationmentioning

confidence: 99%

Section: Talbot Carpets For the Hirota And Hirota-quintic Equationmentioning

confidence: 99%

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Talbot carpets by rogue waves of extended nonlinear Schrödinger equations

et al. 2019

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“…Different from linear periodic structures that have been extensively studied, only a little work has been focused on nonlinear elastic wave metamaterials. Some special properties can be found in these nonlinear periodic structures, e.g., amplitude-dependent band gap [18,19], second harmonics [20][21][22], discrete breathers [23][24][25], solitons [26,27], etc. An interesting phenomenon worth mentioning is the nonreciprocal transmission [28,29], which is due to the breaking reciprocal theorem in wave system [30,31] and behaves as mechanical diodes [32,33].…”

Section: Introductionsmentioning

confidence: 99%

Nonreciprocal Head-on Collision Between Two Nonlinear Solitary Waves in Granular Metamaterials with an Interface

Wang

2021

Acta Mech. Solida Sin.

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In this work, the head-on collision and transmission with nonreciprocal properties of opposite propagating solitary waves are studied, in which the interface between different granular chains is considered. Due to the discontinuity of two periodic granular systems, the transmitted and reflected solitary waves are produced. The head-on collision appears at the interface and the reductive perturbation method is applied to derive the generated solitary waves. According to the derivation and numerical simulation, we can find that the transmitted and reflected solitary waves can propagate with the same speed when they locate at the same chain. Moreover, the influences of both the arrangement and prestress are discussed. It is found that the amplitude and velocity of solitary waves become larger because of a bigger prestress, which result in the nonreciprocal collision and transmission in the granular mechanical metamaterials. This study is expected to be helpful for the design and application of elastic wave metamaterials and mechanical diodes with nonlinear solitary waves.

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Two-breather solutions for the class I infinitely extended nonlinear Schrödinger equation and their special cases

Crabb

Akhmediev

2019

Nonlinear Dyn

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We derive the two-breather solution of the class I infinitely extended nonlinear Schrödinger equation. We present a general form of this multi-parameter solution that includes infinitely many free parameters of the equation and free parameters of the two-breather components. Particular cases of this solution include rogue wave triplets, and special cases of 'breather-tosoliton' and 'rogue wave-to-soliton' transformations. The presence of many parameters in the solution allows one to describe wave propagation problems with higher accuracy than with the use of the basic NLSE.

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Breathers, solitons and rogue waves of the quintic nonlinear Schrödinger equation on various backgrounds

Cited by 25 publications

References 37 publications

Talbot carpets by rogue waves of extended nonlinear Schrödinger equations

Talbot carpets by rogue waves of extended nonlinear Schrödinger equations

Nonreciprocal Head-on Collision Between Two Nonlinear Solitary Waves in Granular Metamaterials with an Interface

Two-breather solutions for the class I infinitely extended nonlinear Schrödinger equation and their special cases

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