Odd-Soliton-Like Solutions for the Variable-Coefficient Variant Boussinesq Model in the Long Gravity Waves

Wang, Lei; Gao, Yi–Tian; Gai, Xiao-Ling

doi:10.1515/zna-2010-1008

Cited by 39 publications

(5 citation statements)

References 18 publications

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“…Relevant issues can be seen in refs. [24][25][26]. Note that the parameters α and β are real constants (we will take α = 1 and β = 2 as examples in all the following analysis), while the wave numbers a 1 and a 2 are arbitrary complex constants.…”

Section: IImentioning

confidence: 99%

Novel behavior and properties for the nonlinear pulse propagation in optical fibers

Lü¹,

Tian²

2012

EPL

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In an integrable generalization of the nonlinear Schrödinger equation for nonlinear pulse propagation in monomode optical fibers, certain higher-order nonlinear effects are taken into account. Hereby for such a model, our investigation focuses on the following aspects: a) modulation instability analysis of solutions in the presence of a small perturbation; b) derivation of the infinite conservation laws based on the Lax pair; c) soliton solutions obtained in virtue of the bilinear method with symbolic computation; d) asymptotic analysis and graphical illustration of the solitons. With different choices of the wave numbers in the two-soliton solutions, solitonic characteristics has been discussed. Finally a new type of soliton, namely the "earthwormon", has been proposed in that the moving two-soliton structure looks like an earthworm in slice graphics.

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Section: IImentioning

confidence: 99%

Novel behavior and properties for the nonlinear pulse propagation in optical fibers

Lü¹,

Tian²

2012

EPL

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“…Through the similar analysis to expressions (20) and (21), we could also derive that the interaction among the three solitons is elastic. Relevant issues can also be seen in [58][59][60][61][62]. (a) a 0 = 2, λ = 0.05, q 1 = 1, q 1 = 1, 1 = −1, 1 = 0, q 2 = 0.5, q 2 = 0, 2 = −2, 2 = 0, q 3 = 1, q 3 = 0, 3 = 10, and 3 = 0; (b) a 0 = 2, λ = 0.05, q 1 = 1, q 1 = 0, 1 = −1, 1 = 1, q 2 = 0.8, q 2 = 0.8, 2 = −5, 2 = 0, q 3 = 1.5, q 3 = −1.5, 3 = 20, F and 3 = 0…”

Section: Soliton Interaction Propertiesmentioning

confidence: 99%

Soliton dynamics and interaction in the Bose–Einstein condensates with harmonic trapping potential and time-varying interatomic interaction

et al. 2011

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Investigated in this paper is the quasi-onedimensional Gross-Pitaevskii equation, which describes the dynamics of the Bose-Einstein condensates with the harmonic trapping potential and timevarying interatomic interaction. Via the Horita method and symbolic computation, analytic bright N-soliton solution is obtained. One-, two-and three-soliton solutions are analyzed graphically. Based on the limit analysis on the one-and two-soliton solutions, the modulation on the speed of the matter-wave bright solitons is realized. Via the parameters, the interaction between the matter-wave solitons are adjustable. Furthermore, an approach to construct the interference between the matter-wave solitons has been proposed. Finally, investigation on the three-soliton solution verifies our conclusions drawn from the one and two solitons. Our conclusions might be useful in the fields of the control on the matter-wave solitons, atom lasers, and atomic accelerators.

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“…In the next section, with symbolic computation [34][35][36][37][38][39], (a) we will firstly apply the Darboux transformation (DT) to derive the bright one-and two-soliton solutions for System (1); (b) through the asymptotic analysis for the two-soliton solution, energy-exchange soliton collisions with partial or complete energy exchange will be examined; (c) the first three conservation laws for System (1) will be obtained. At last, the conclusions will be addressed in Sect.…”

Section: Introductionmentioning

confidence: 99%

Soliton interactions in a generalized inhomogeneous coupled Hirota–Maxwell–Bloch system

Xue

Tian

et al. 2011

Nonlinear Dyn

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In this paper, via the Darboux transformation, with symbolic computation, the bright oneand two-soliton solutions for a generalized inhomogeneous coupled Hirota-Maxwell-Bloch system are obtained in an inhomogeneous nonlinear dispersive fiber doped with two-level resonant atoms. The study on the bright soliton collision shows that in this system, there exists the complete or partial energy exchange. Through the asymptotic analysis, some physical quantities are discussed. Energy transfer in the two-soliton collision might have potential applications in the study of pulse amplification. In addition, the conservation laws for the system are also constructed.

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Odd-Soliton-Like Solutions for the Variable-Coefficient Variant Boussinesq Model in the Long Gravity Waves

Cited by 39 publications

References 18 publications

Novel behavior and properties for the nonlinear pulse propagation in optical fibers

Novel behavior and properties for the nonlinear pulse propagation in optical fibers

Soliton dynamics and interaction in the Bose–Einstein condensates with harmonic trapping potential and time-varying interatomic interaction

Soliton interactions in a generalized inhomogeneous coupled Hirota–Maxwell–Bloch system

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