Dust ion-acoustic rogue waves in a three-species ultracold quantum dusty plasmas

Sun, Wen‐Rong; Tian, Bo; Liu, Rong-Xiang; Liu, De-Yin

doi:10.1016/j.aop.2014.06.023

Cited by 27 publications

(28 citation statements)

References 48 publications

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“…In this section, we present the generalised DT for (2). With the 2 × 2 Ablowitz-Kaup-Newell-Segur (AKNS) scheme, the Lax pair associated with (2) has been given as [9] , ,…”

Section: Generalised Dt For Equation (2)mentioning

confidence: 99%

“…With the 2 × 2 Ablowitz-Kaup-Newell-Segur (AKNS) scheme, the Lax pair associated with (2) has been given as [9] , ,…”

Section: Generalised Dt For Equation (2)mentioning

confidence: 99%

“…Rogue waves, also known as the freak waves or monster waves, have been used to describe the isolated and large waves with higher amplitudes than the average wave crests around in the ocean and have also been seen in the Bose-Einstein condensates, plasmas, and optical fibres [1][2][3][4][5][6]. A model for the rogue waves in optical fibre communication is the 'self-focusing' nonlinear Schrödinger (NLS) equation [7,8], 2 1 | | 0, 2…”

Section: Introductionmentioning

confidence: 99%

“…A model for the rogue waves in optical fibre communication is the 'self-focusing' nonlinear Schrödinger (NLS) equation [7,8], 2 1 | | 0, 2…”

Section: Introductionmentioning

confidence: 99%

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Higher-Order Rogue Waves for a Fifth-Order Dispersive Nonlinear Schrödinger Equation in an Optical Fibre

Wang

Gao

et al. 2015

Zeitschrift Für Naturforschung A

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In this article, a fifth-order dispersive nonlinear Schrödinger equation is investigated, which describes the propagation of ultrashort optical pulses, up to the attosecond duration, in an optical fibre. Rogue wave solutions are derived by virtue of the generalised Darboux transformation. Rogue wave structures and interaction are discussed through (i) the analyses on the higher-order rogue waves, the cubic, quartic, quintic, group-velocity, and phaseparameter effects; (ii) a higher-order rogue wave consisting of the first-order rogue waves via the interaction; (iii) characteristics of the rogue waves which are summarised, including the maximum/minimum values of the rogue waves and the number of the first-order rogue waves for composing the higher-order rogue wave; and (iv) spatialtemporal patterns which are illustrated and compared with those of the 'self-focusing' nonlinear Schrödinger equation. We find that the quintic terms increase the time of appearance for the first-order rogue waves which form the higher-order rogue wave, and that the quintic terms affect the interaction among the first-order rogue waves, which elongates the distance of appearance for the higherorder rogue wave.

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“…In this section, we present the generalised DT for (2). With the 2 × 2 Ablowitz-Kaup-Newell-Segur (AKNS) scheme, the Lax pair associated with (2) has been given as [9] , ,…”

Section: Generalised Dt For Equation (2)mentioning

confidence: 99%

“…With the 2 × 2 Ablowitz-Kaup-Newell-Segur (AKNS) scheme, the Lax pair associated with (2) has been given as [9] , ,…”

Section: Generalised Dt For Equation (2)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…A model for the rogue waves in optical fibre communication is the 'self-focusing' nonlinear Schrödinger (NLS) equation [7,8], 2 1 | | 0, 2…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Higher-Order Rogue Waves for a Fifth-Order Dispersive Nonlinear Schrödinger Equation in an Optical Fibre

Wang

Gao

et al. 2015

Zeitschrift Für Naturforschung A

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“…Besides, for (1), multi-periodic solutions [12], variable-separation solutions [13,14], and soliton-like solutions [15] have been obtained. Conversely, integrable versions of the NLEEs usually have the soliton solutions [16][17][18][19][20]. A soliton is a solitary wave which preserves its velocity and shape after the interaction [7], i.e., the soliton can be considered as a quasiparticle [21,22].…”

Section: Introductionmentioning

confidence: 99%

On a (3+1)-dimensional Boiti–Leon–Manna–Pempinelli Equation

Zuo¹,

Gao

et al. 2015

Zeitschrift Für Naturforschung A

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The Boiti-Leon-Manna-Pempinelli (BLMP) equation is seen as a model for the incompressible fluid. In this article, a (3+1)-dimensional BLMP equation is investigated. With the aid of the Bell polynomials, bilinear form of such an equation is obtained. By virtue of the bilinear form, two kinds of soliton solutions with different nonlinear dispersion relations and another kind of analytic solutions are derived. Lax pairs and Bäcklund transformations are also constructed. Soliton propagation and interaction are analysed: (i) solitions with different nonlinear dispersion relations have different velocities and backgrounds; (ii) for another kind of analytic solutions with different nonlinear dispersion relations, the periodic property is displayed.

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Numerous Analytical Solutions to a (2 + 1)-Dimensional Schrödinger Equation with Variable Coefficients in Inhomogeneous Media

Wang,

Gao

2024

Int. J. Appl. Comput. Math

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Dust ion-acoustic rogue waves in a three-species ultracold quantum dusty plasmas

Cited by 27 publications

References 48 publications

Higher-Order Rogue Waves for a Fifth-Order Dispersive Nonlinear Schrödinger Equation in an Optical Fibre

Higher-Order Rogue Waves for a Fifth-Order Dispersive Nonlinear Schrödinger Equation in an Optical Fibre

On a (3+1)-dimensional Boiti–Leon–Manna–Pempinelli Equation

Numerous Analytical Solutions to a (2 + 1)-Dimensional Schrödinger Equation with Variable Coefficients in Inhomogeneous Media

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