Rogue wave solutions for the coupled cubic–quintic nonlinear Schrödinger equations in nonlinear optics

Zhang, Yan; Nie, Xian-Jia; Zhaqilao, Zhaqilao

doi:10.1016/j.physleta.2013.11.010

Cited by 36 publications

(19 citation statements)

References 22 publications

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“…This completes the proof of Proposition 1. By virtue of the above formulae (37) and (38), we can obtain concrete expressions of the modules for the second-order localized wave solutions. Here, we omit presenting the expressions since they are rather cumbersome to write down.…”

Section: The Second-order Localized Wave Solutionsmentioning

confidence: 99%

Localized waves of the coupled cubic–quintic nonlinear Schrödinger equations in nonlinear optics

Chen

Lin

2017

Chinese Phys. B

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We investigate some novel localized waves on the plane wave background in the coupled cubic-quintic nonlinear Schrödinger (CCQNLS) equations through the generalized Darboux transformation (DT). A special vector solution of the Lax pair of the CCQNLS system is elaborately constructed, based on the vector solution, various types of higherorder localized wave solutions of the CCQNLS system are constructed via the generalized DT. These abundant and novel localized waves constructed in the CCQNLS system include higher-order rogue waves, higher-order rogues interacting with multi-soliton or multi-breather separately. The first-and second-order semi-rational localized waves including several free parameters are mainly discussed: (i) the semi-rational solutions degenerate to the first-and second-order vector rogue wave solutions; (ii) hybrid solutions between a first-order rogue wave and a dark or bright soliton, a second-order rogue wave and two dark or bright solitons; (iii) hybrid solutions between a first-order rogue wave and a breather, a second-order rogue wave and two breathers. Some interesting and appealing dynamic properties of these types of localized waves are demonstrated, for example, these nonlinear waves merge with each other markedly by increasing the absolute value of α. These results further uncover some striking dynamic structures in the CCQNLS system.

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Section: The Second-order Localized Wave Solutionsmentioning

confidence: 99%

Localized waves of the coupled cubic–quintic nonlinear Schrödinger equations in nonlinear optics

Chen

Lin

2017

Chinese Phys. B

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“…Lax pair can assure the integrability of a nonlinear system, from which the initial problem of a given NLEE can be solved, and the integrable property such as conservation law, symmetry class, Hamiltonian structure, and DT can be derived [36][37][38][39][40][41]. Based on the Lax pair of System (3), the associated linear eigenvalue problem of the equation can be expressed as…”

Section: Elementary Darboux Transformation Of System (3)mentioning

confidence: 99%

“…3, can be used to interpret the formation of rogue waves [21][22][23]. By virtue of the generalized DT and Taylor expansion of those solutions for the associated Lax pair [39][40][41], the rogue wave solutions for System (3) can be derived. Supposing that ψ = φ 1 (λ + δ) is a special solution of Lax pair (4) and (5), where δ is a small parameter, the function ψ can be expanded into the Taylor series of δ…”

Section: The Generalized Dt For System (3)mentioning

confidence: 99%

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Breather and rogue wave solutions for a nonlinear Schrödinger-type system in plasmas

Meng

Qin

2015

Nonlinear Dyn

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A nonlinear Schrödinger equation with self-consistent sources can be used to describe the interaction between an high-frequency electrostatic wave and an ion-acoustic wave in two-component homogeneous plasmas. In this paper, breather and rogue waves solutions for such a system are investigated via the Darboux transformation. The spatially and temporally periodic breathers have been found. When the cubic nonlinearity coefficient and the background amplitude are varied, the propagating trajectories of breather are changed. The interaction between two breathers are also studied, which shows that when the wave numbers are close, the two breathers are partially coalesced. All of the first-, second-, and third-order rogue waves present certain lumps or valleys around a center in the temporal-spatial distribution, and the peak heights of the ion-acoustic waves are more than three times those of the background. However, for the high-frequency electrostatic waves, the values around the centers are less than the background intensity.

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“…This problem was initially considered in hydrodynamics and was later extended to other fields of physics [1][2][3][4][5][6][7].…”

Section: Introductionmentioning

confidence: 99%

Pressure induced breather overturning on deep water: Exact solution

Abrashkin

Oshmarina

2014

Physics Letters A

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Rogue wave solutions for the coupled cubic–quintic nonlinear Schrödinger equations in nonlinear optics

Cited by 36 publications

References 22 publications

Localized waves of the coupled cubic–quintic nonlinear Schrödinger equations in nonlinear optics

Localized waves of the coupled cubic–quintic nonlinear Schrödinger equations in nonlinear optics

Breather and rogue wave solutions for a nonlinear Schrödinger-type system in plasmas

Pressure induced breather overturning on deep water: Exact solution

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