An explicit expression of the dark N-soliton solution of the MKdV equation by means of the Darboux transformation

Chen, Zongyun; Huang, Nian-Ning; Liu, Zhongzhu; Xiao, Yi

doi:10.1088/0305-4470/26/6/018

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Cited by 5 publications

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“…The same solutions also apply to (18) with dispersion (50). These solutions with a constant background are known as dark solitons [21,22]. Dark solitons of the NLS equation have a wide application in nonlinear optics.…”

Section: Examplesmentioning

confidence: 99%

Nonvanishing boundary condition for the mKdV hierarchy and the Gardner equation

Gomes¹,

França²,

Zímerman³

2011

J. Phys. A: Math. Theor.

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A Kac-Moody algebra construction for the integrable hierarchy containing the Gardner equation is proposed. Solutions are systematically constructed employing the dressing method and deformed vertex operators which takes into account the nonvanishing boundary value problem for the mKdV hierarchy. Explicit examples are given and besides usual KdV like solitons, our solutions contemplate the large amplitude table-top solitons, kinks, dark solitons, breathers and wobbles.

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Section: Examplesmentioning

confidence: 99%

Nonvanishing boundary condition for the mKdV hierarchy and the Gardner equation

Gomes¹,

França²,

Zímerman³

2011

J. Phys. A: Math. Theor.

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show abstract

“…A Darboux transformation was developed for generating dark multi-soliton solutions of the mKdV equation [11]. Based on the factorization of soliton equations into two commuting integrable x-and t-constrained flows, Ref.…”

Section: Introductionmentioning

confidence: 99%