Alfven solitons

Huang, Nian-Ning; Chen, Zongyun

doi:10.1088/0305-4470/23/4/014

Cited by 55 publications

(44 citation statements)

References 9 publications

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“…Soliton solutions for the DNLS equation with VBC, including one-soliton solution [17] and multi-soliton formulas(e.g., [18,19]), have been known. Researches on the DNLS equation with NVBC showed that its general onesoliton solution (corresponding to a complex discrete spectral parameter) is a breather which degenerates to a pure bright or dark soliton when the discrete spectral parameter becomes purely imaginary [20,21,4,5,22].…”

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confidence: 99%

N-soliton solution for the derivative nonlinear Schrödinger equation with nonvanishing boundary conditions

Chen¹,

Yang²,

Lam³

2006

J. Phys. A: Math. Gen.

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An explicit two-soliton solution for the derivative nonlinear Schrödinger equation with nonvanishing boundary conditions is derived, demonstrating details of interactions between two bright solitons, two dark solitons, as well as one bright soliton and one dark soliton. Shifts of soliton positions due to collisions are analytically obtained, which are irrespective of the bright or dark characters of the participating solitons. The derivative nonlinear Schrödinger (DNLS) equation is an integrable model describing various nonlinear waves such as nonlinear Alfvén waves in space plasma(see, e.g., [1,2,3,4,5,6,7]), sub-picosecond pulses in single mode optical fibers(see, e.g., [8,9,10,11,12]), and weak nonlinear electromagnetic waves in ferromagnetic [13], antiferromagnetic [14], and dielectric[15] systems under external magnetic fields. Both of vanishing boundary conditions (VBC) and nonvanishing boundary conditions (NVBC) for the DNLS equation are physically significant. For problems of nonlinear Alfvén waves, weak nonlinear electromagnetic waves in magnetic and dielectric media, waves propagating strictly parallel to the ambient magnetic fields are modelled by VBC while those oblique waves are modelled by NVBC. In optical fibers, pulses under bright background waves are modelled by NVBC.

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confidence: 99%

N-soliton solution for the derivative nonlinear Schrödinger equation with nonvanishing boundary conditions

Chen¹,

Yang²,

Lam³

2006

J. Phys. A: Math. Gen.

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“…The first N-soliton formula for the DNLS equation was obtained by Nakamura and Chen [19] by use of Hirota's bilinear transform method. On the basis of Darboux transformation, another alternative method, Huang and Chen [11] established an N-soliton formula in terms of determinants. Darboux transformations are an important tool for studying the solutions of integrable systems.…”

Section: Introductionmentioning

confidence: 99%

On Darboux transformations for the derivative nonlinear Schrödinger equation

Nimmo¹,

Yilmaz²

2021

JNMP

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“…On the basis of bilinear transformation, the first N-solition formula was obtained by Nakamuro and Chen [11]. Determinant expression of the N-soliton solution can be established via applying the Darboux transformation [12]. In the case of the non-vanishing boundary condition(NVBC), Kawata and Inoue developed an IST for the DNLS equation and obtained a breather-type soliton (paired soliton) [13].…”

Section: Introductionmentioning

confidence: 99%