Soliton, breather and rogue wave solutions of the coupled Gerdjikov–Ivanov equation via Darboux transformation

Ji, Ting; Zhai, Yunyun

doi:10.1007/s11071-020-05790-5

Cited by 37 publications

(11 citation statements)

References 54 publications

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“…In this paper, an N -coupled HNLS system (N is a positive integer), i.e., System (1) which describes the properties of the ultrashort optical pulses in an optical fiber, has been investigated. System (1) has been converted into System (3) through Variable Transformation (2). Based on the (2N +1)th-order Lax Pair (4) of System (3), DT (5) for System (1) has been constructed, which demands that the first element φ 1 in the eigenfunction Φ is real and complex spectral parameter λ 1 = iη 1 is a pure imaginary number.…”

Section: Discussionmentioning

confidence: 99%

“…We find that δ hC do not affect the modulus value of u [2] j in Solution (22). Then, we let δ hC equal to 0 without affecting our following analysis.…”

Section: Evolution and Interaction Between The Two Bright Solitonsmentioning

confidence: 99%

“…Since System (1) and System (3) can be converted to each other through Variable Transformation (2), we can get the solutions of System (3) first, then perform Variable Transformation (2) and get the solutions of System (1).…”

Section: Dt Of System (1)mentioning

confidence: 99%

“…Nonlinear evolution equations have been used to describe the physical phenomena in fluid mechanics, fiber optics, biochemistries and plasma physics [1][2][3][4][5][6][7]. Solitons, as a kind of solution of the nonlinear evolution equations, have attracted the attention of the researchers [8,9].…”

Section: Introductionmentioning

confidence: 99%

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Darboux transformation, bright and dark–bright solitons of an N-coupled high-order nonlinear Schrödinger system in an optical fiber

Gao

Ding

et al. 2022

Mod. Phys. Lett. B

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In this paper, an [Formula: see text]-coupled high-order nonlinear Schrödinger system, which describes the properties of the ultrashort optical pulses in an optical fiber, is investigated with the Darboux transformation (DT) method and asymptotic analysis. Starting from the given [Formula: see text]th-order Lax pair, we construct a new form of the DT (with some complex eigenfunctions of a Lax pair involved) to derive the formulas of the [Formula: see text]th-iterated solutions, where [Formula: see text] and [Formula: see text] are the positive integers. On the zero background, the first- and second-order solitons are obtained and analyzed through the asymptotic analysis. Multi-parameter adjustment is proceeded since there are [Formula: see text] real parameters in the second-order solitons. We find that under certain conditions each of the two interaction patterns (elastic and/or inelastic) holds in the second-order solitons. On the plane wave background, the first-order bright and dark–bright solitons are obtained. Velocities, amplitudes, widths and characteristic lines of the first-order bright and dark–bright solitons are presented and analyzed.

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Section: Discussionmentioning

confidence: 99%

“…We find that δ hC do not affect the modulus value of u [2] j in Solution (22). Then, we let δ hC equal to 0 without affecting our following analysis.…”

Section: Evolution and Interaction Between The Two Bright Solitonsmentioning

confidence: 99%

Section: Dt Of System (1)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Darboux transformation, bright and dark–bright solitons of an N-coupled high-order nonlinear Schrödinger system in an optical fiber

Gao

Ding

et al. 2022

Mod. Phys. Lett. B

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“…Rogue waves (RWs) with a variety of properties have been uncovered as a hot research topic in recent years. It first appeared in the deep ocean in the form of an extremely destructive wave, surprisingly, RWs have also been found in various physical systems, such as optical fiber systems, water fluids, plasma, Bose-Einstein condensates and even financial systems [11][12][13][14][15][16][17][18][19], etc., which are currently more popular. There is a consensus in the current study of RWs that they are produced by tuning to modulation instability (MI) waves, and the breather solution involved in them usually come from instabilities with small amplitude perturbations, the magnitude of which has the potential to affect the degree of catastrophe suffered.…”

Section: Modulation Instability Localized Wave Solutions Of the Modif...mentioning

confidence: 99%

Modulation instability, localized wave solutions of the modified Gerdjikov–Ivanov equation with anomalous dispersion

et al. 2023

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Solving new integrable systems and exploring their physical applications have been a hot topic. This paper gives the modulation instability in the continuous wave background of the new modified Gerdjikov-Ivanov equation with anomalous dispersion. Based on the extend Lax pair, the localized wave solutions of the new model are obtained via generalized Darboux transformation method, various types solutions including breather, rogue waves, interaction solutions are presented and their dynamic properties are analyzed. The results obtained have certain application value for nonlinear optics and long-distance transmission.

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Localized wave solutions to the vector nonlinear Schrödinger equation with nonzero backgrounds

Zhai

et al. 2023

Math Methods in App Sciences

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The vector nonlinear Schrödinger (NLS) system is studied through the generalized Darboux transformation (DT). We begin with the nonzero seed solution in the exponential form of evolution variable and explore the eigenfunction of the ‐component NLS equation. With the formulae of the eigenfunction, localized wave solutions of the two‐component and three‐component NLS equations are studied. By choosing different free parameters, some special solutions and the dynamic evolutions are presented, including breather–rogue wave, breather fission, breather fusion, and breather–soliton.

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Soliton, breather and rogue wave solutions of the coupled Gerdjikov–Ivanov equation via Darboux transformation

Cited by 37 publications

References 54 publications

Darboux transformation, bright and dark–bright solitons of an N-coupled high-order nonlinear Schrödinger system in an optical fiber

Darboux transformation, bright and dark–bright solitons of an N-coupled high-order nonlinear Schrödinger system in an optical fiber

Modulation instability, localized wave solutions of the modified Gerdjikov–Ivanov equation with anomalous dispersion

Localized wave solutions to the vector nonlinear Schrödinger equation with nonzero backgrounds

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