Rational W-shaped solitons on a continuous-wave background in the Sasa-Satsuma equation

Zhao, Li-Chen; Li, Sheng-Chang; Ling, Liming

doi:10.1103/physreve.89.023210

Cited by 84 publications

(49 citation statements)

References 33 publications

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“…What should be pointed out that, most of the single localized wave solutions have been obtain in the previous literature. For the focusing case, the breather solution [1,30], rogue wave solution [4], rational W-shape soliton [34] and degenerate resonant soliton on NVBC [32] have been obtained in the previous literature. For the defocusing case, the dark soliton and W-shape dark soliton (dark double-hump soliton) have been been obtain through bilinear method and symbolic computation [12].…”

Section: 1mentioning

confidence: 99%

The algebraic representation for high order solution of Sasa-Satsuma equation

Ling¹

2016

DCDS-S

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In this paper, we reestablish the elementary Darboux transformation for Sasa-Satsuma equation with the aid of loop group method. Furthermore, the generalized Darboux transformation is given with the limit technique. As direct applications, we give the single solitonic solutions for the focusing and defocusing case. The general high order solution formulas with the determinant form are obtained through generalized DT and the formal series method. 1975 1976 LIMING LING then equation (2) could be rewritten asSSE (4) is one of a limited number of integrable models and has been a field of active research for the past two decades. Thanks to the integrability, the sophisticated soliton construct underlying this wave equation can, therefore, be achieved using an array of mathematical tools such as inverse scattering transform [22,14,17,33], Darboux transformation (DT) [27,30,1,4,32,25], Hirota bilinear method [6,5,26], and others. Although the DT for the SSE was given in the previous study, the reduction of DT is not complete. In this work, we reestablish the DT through the loop group method [29]. With this way, we can obtain the DT completely. On the other hand, since the spectral problem for SSE (4) is 3 × 3 and possesses deep reduction, the high order DT can not be obtained directly. Based on the elementary DT [21,7] and analysis of spectral parameters, one can obtain the generalized DT [2,9,10,19]. As direct applications, the single solitonic solutions, multi-solitonic solution and the high order solitonic solutions are given through this method.In the previous literature, most of works concentrate on the soliton solution for SSE on the zero background [27,28]. Recently, there are some works focus on the solutions of SSE with the non-vanishing background (NVBC). For instance: the breather solution [30, 1], W-shape soliton [32], rational W-shape soliton [34] and the twist rogue wave solution [4] are obtained for the focusing SSE in the recent literature. In this work, we construct the solitonic solution for both the focusing and defocusing SSE on the NVBC systematically. For the focusing case, when the spectral parameter is located in the image axis, we can obtain the soliton solution and resonant soliton solution, periodical solution, half periodical solution, rational W-shape soliton, resonant rational W-shape soliton, and their high order ones; when the spectral parameter is not located in the image and real axis, we can obtain the breather solution, resonant breather solution, rogue wave solution, composite rogue wave solution and their high order ones. For the defocusing case, when the spectral parameter is located on the segment of real axis, we can obtain the dark soliton, W-shape dark soliton; when the spectral parameter is not located on the real and image axis, we can obtain the breather solution and its high order ones.The structure of this paper is organized in the following: In section 2, we give the DT and generalized DT for SSE through the loop group method. The reduction for DT was analyzed by spectral...

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Section: 1mentioning

confidence: 99%

The algebraic representation for high order solution of Sasa-Satsuma equation

Ling¹

2016

DCDS-S

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“…1 (c)], and anti-eye-shaped one [ Fig. 2 [26,27]; otherwise, the rational solution demonstrates W-shaped soliton behavior [28] for the nonlnear fiber with high-order effects. It was also demonstrated that relative frequency can vary MI properties and induced RWs in coupled defocusing NLS [29].…”

Section: Spectrum Analysis Of Different Rogue Wave Patternsmentioning

confidence: 99%

Rogue-wave pattern transition induced by relative frequency

2014

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We revisit a rogue wave in a two-mode nonlinear fiber whose dynamics is described by two-component coupled nonlinear Schrödinger equations. The relative frequency between two modes can induce different rogue wave patterns transition. In particular, we find a four-petaled flower structure rogue wave can exist in the two-mode coupled system, which possesses an asymmetric spectrum distribution. Furthermore, spectrum analysis is performed on these different type rogue waves, and the spectrum relations between them are discussed. We demonstrate qualitatively that different modulation instability gain distribution can induce different rogue wave excitation patterns. These results would deepen our understanding of rogue wave dynamics in complex systems.

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“…During the past few decades, the cosmological principle had been tested many times and found to be well consistent with most cosmological observations, for instance, the halo power spectrum [2], the statistics of galaxies [3], the cosmic microwave background (CMB) radiation from Wilkinson Microwave Anisotropy Probe (WMAP) [4,5] and Planck satellites [6][7][8]. However, there still exist some phenomena which are inconsistent with the cosmological principle, such as the alignment of quasar polarization vectors on large scale [9], the spatial variation of the fine structure constant [10,11] and MOND acceleration scale [12][13][14], the anisotropic accelerating expansion of the Universe [15][16][17][18][19][20], the alignment of CMB quadrupole and octopole [21][22][23], the hemispherical power asymmetry in CMB [24][25][26][27], and parity asymmetry in CMB [26][27][28][29][30][31]. In particular, hemispherical power asymmetry, initially observed in WMAP [4,5], has come to be one of the outstanding anomalies that indicated violation of statistical isotropy on large angular scales of CMB sky.…”

Section: Introductionmentioning

confidence: 99%

Constraining the anisotropy of the Universe with the Pantheon supernovae sample *

2019

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We test the possible dipole anisotropy of a Finslerian cosmological model and other three dipolemodulated cosmological models, i.e., the dipole-modulated ΛCDM, wCDM and Chevallier-Polarski-Linder (CPL) model by using the recently released Pantheon sample of SNe Ia. The Markov chain Monte Carlo (MCMC) method is used to explore the whole parameter space. We find that the dipole anisotropy is very weak in all cosmological models used. Although the dipole amplitudes of four cosmological models are consistent with zero within 1σ uncertainty, the dipole directions are close to the axial direction to the plane of SDSS subsample among Pantheon. It may imply that the weak dipole anisotropy in the Pantheon sample originates from the inhomogeneous distribution of the SDSS subsample. More homogeneous distribution of SNe Ia is necessary to constrain the cosmic anisotropy.

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Rational W-shaped solitons on a continuous-wave background in the Sasa-Satsuma equation

Cited by 84 publications

References 33 publications

The algebraic representation for high order solution of Sasa-Satsuma equation

The algebraic representation for high order solution of Sasa-Satsuma equation

Rogue-wave pattern transition induced by relative frequency

Constraining the anisotropy of the Universe with the Pantheon supernovae sample *

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