Soliton solutions for a perturbed nonlinear Schrodinger equation

We study the properties of the chaotic wave fields generated in the frame of the Sasa-Satsuma equation (SSE). Modulation instability results in a chaotic pattern of small-scale filaments with a free parameter-the propagation constant k. The average velocity of the filaments is approximately given by the group velocity calculated from the dispersion relation for the plane-wave solution. Remarkably, our results reveal the reason for the skewed profile of the exact SSE rogue-wave solutions, which was one of their distinctive unexplained features. We have also calculated the probability density functions for various values of the propagation constant k, showing that probability of appearance of rogue waves depends on k.

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“…There is a number of publications dealing with the solutions of the SSE [33][34][35][36][37][38][39]. The form of Eq.…”

Section: Introductionmentioning

confidence: 99%

“…The form of Eq. (1) has been used in a series of works by Mihalache et al [33][34][35]. The form of the SSE in the work by Wright III [36] is slightly different from the original version:…”

Section: Introductionmentioning

confidence: 99%

Rogue waves of the Sasa-Satsuma equation in a chaotic wave field

et al. 2014

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“…In this case, the generalized NLS equation (2) under (24) can also include Sasa-Satsuma (SS) equation [47][48][49][50][51][52] Fig. 3 The second-order rogue wave (23) under the free functions given by (22) with α = 1, ε = 3, ε 2 = 0.1, ρ 0 = 1, χ 0 = 2, χ 1 = 0.6, w 0 = 0.01, β 0 = 0.1, a = 0.15 and β = 100: a The motions of the hump and valleys; b the value evolutions of the hump and valleys; c the 2D contour plot; d the density evolution of the rogue wave Fig.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Optical temporal rogue waves in the generalized inhomogeneous nonlinear Schrödinger equation with varying higher-order even and odd terms

2015

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We investigate optical temporal rogue waves of the generalized nonlinear Schrödinger (NLS) equation with higher-order odd and even terms and space-and time-modulated coefficients, which includes the NLS equation, Lakshmanan-Porsezian-Daniel (LPD) equation, Hirota equation, Chen-Lee-Liu equation, and Kaup-Newell derivative NLS equation. Based on the similarity reduction method, the generalized NLS equation can be reduced to the integrable LPDHirota equation under a set of constraint conditions, from which the solutions of generalized NLS equation can be obtained in the basis of solutions of the LPDHirota equation and the similarity transformation. In particular, the first-and second-order self-similar rogue wave solutions of the generalized NLS equation are derived under different parameters, and the contour profiles and density evolutions of self-similar rogue wave solutions are given to study their wave structures and dynamic properties. At the same time, the motions of the hump and valleys related to the self-similar rogue waves are also given, from which we can control and manage the self-similar rogue waves by adjusting the third-order dispersion term. These results may be useful in nonlinear optics and related fields. KeywordsThe generalized nonlinear Schrödinger (NLS) equation · The LPD-Hirota equation · Similarity reduction method · Rogue wave solutions · Motions of the hump and valleys

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“…We note that this has similar x, t-dependence as (19) but the functional form is different, also in the limit a → 0, i.e., κ → 0 we obtain the real limit (20). It turns out that (21) is still not the most general one-soliton solution for this system, it is given by q = G/F , where…”

Section: E Traveling-wave Solutionsmentioning

confidence: 64%

Sasa-Satsuma higher-order nonlinear Schrödinger equation and its bilinearization and multisoliton solutions

et al. 2003

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Higher order and multicomponent generalizations of the nonlinear Schrödinger equation are important in various applications, e.g., in optics. One of these equations, the integrable Sasa-Satsuma equation, has particularly interesting soliton solutions. Unfortunately the construction of multisoliton solutions to this equation presents difficulties due to its complicated bilinearization. We discuss briefly some previous attempts and then give the correct bilinearization based on the interpretation of the Sasa-Satsuma equation as a reduction of the three-component Kadomtsev-Petviashvili hierarchy. In the process we also get bilinearizations and multi-soliton formulae for a two component generalization of the Sasa-Satsuma equation (the Yajima-Oikawa-Tasgal-Potasek model), and for a (2 + 1)-dimensional generalization.

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Soliton solutions for a perturbed nonlinear Schrodinger equation

Cited by 53 publications

References 31 publications

Rogue waves of the Sasa-Satsuma equation in a chaotic wave field

Rogue waves of the Sasa-Satsuma equation in a chaotic wave field

Optical temporal rogue waves in the generalized inhomogeneous nonlinear Schrödinger equation with varying higher-order even and odd terms

Sasa-Satsuma higher-order nonlinear Schrödinger equation and its bilinearization and multisoliton solutions

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