Darboux transformation and multi-soliton solutions of the discrete sine-Gordon equation

Hanif, Y.; Saleem, U.

doi:10.1093/ptep/ptaa068

Cited by 3 publications

(2 citation statements)

References 15 publications

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“…Combining Eqs. ( 4), ( 5) and ( 6), we get U [1] T [1] = T [1] x + T [1] U, V [1] T [1] = T [1] t + T [1] V. (7) We expand Eqs. (7) and let the coefficients of each subterm of λ be zero, then we get…”

Section: Dt Of System (1)mentioning

confidence: 99%

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Darboux transformation, bright and dark–bright solitons of an N-coupled high-order nonlinear Schrödinger system in an optical fiber

Gao

Ding

et al. 2022

Mod. Phys. Lett. B

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In this paper, an [Formula: see text]-coupled high-order nonlinear Schrödinger system, which describes the properties of the ultrashort optical pulses in an optical fiber, is investigated with the Darboux transformation (DT) method and asymptotic analysis. Starting from the given [Formula: see text]th-order Lax pair, we construct a new form of the DT (with some complex eigenfunctions of a Lax pair involved) to derive the formulas of the [Formula: see text]th-iterated solutions, where [Formula: see text] and [Formula: see text] are the positive integers. On the zero background, the first- and second-order solitons are obtained and analyzed through the asymptotic analysis. Multi-parameter adjustment is proceeded since there are [Formula: see text] real parameters in the second-order solitons. We find that under certain conditions each of the two interaction patterns (elastic and/or inelastic) holds in the second-order solitons. On the plane wave background, the first-order bright and dark–bright solitons are obtained. Velocities, amplitudes, widths and characteristic lines of the first-order bright and dark–bright solitons are presented and analyzed.

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Section: Dt Of System (1)mentioning

confidence: 99%

“…Nonlinear evolution equations have been used to describe the physical phenomena in fluid mechanics, fiber optics, biochemistries and plasma physics [1][2][3][4][5][6][7]. Solitons, as a kind of solution of the nonlinear evolution equations, have attracted the attention of the researchers [8,9].…”

Section: Introductionmentioning

confidence: 99%

Darboux transformation, bright and dark–bright solitons of an N-coupled high-order nonlinear Schrödinger system in an optical fiber

Gao

Ding

et al. 2022

Mod. Phys. Lett. B

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show abstract

Bilinear form, solitons, breathers, lumps and hybrid solutions for a (3+1)-dimensional Date-Jimbo-Kashiwara-Miwa equation

Wang

Gao

et al. 2021

Nonlinear Dyn

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Darboux transformation, bright and dark-bright solitons of an N-coupled high-order nonlinear Schrödinger system in an optical fiber

Gao¹,

Yu²,

Ding³

et al. 2021

Preprint

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In this paper, an N -coupled high-order nonlinear Schrödinger system, which describes the properties of the ultrashort optical pulses in an optical fiber, is investigated with the help of Darboux transformation (DT) method and asymptotic analysis. Starting from the given (2 N +1)th-order Lax pair, we construct a new form of DT (complex eigenfunctions of Lax pair involved) to derive the formulas of the n th-iterated solutions, where n and N are the positive integers. On the zero background, the first- and second-order solitons are obtained and analysed through the asymptotic analysis. Multi-parameter adjustment is proceeded since there are 3 N +4 real parameters in the second-order solitons. We find that under certain conditions each of the two interaction patterns (elastic, inelastic) holds in the second-order soliton. On the plane wave background, the first-order bright and dark-bright solitons are obtained. Soliton velocities, amplitudes, widths and characteristic lines of the first-order bright and dark-bright solitons are presented and analysed.

show abstract

Darboux transformation and multi-soliton solutions of the discrete sine-Gordon equation

Cited by 3 publications

References 15 publications

Darboux transformation, bright and dark–bright solitons of an N-coupled high-order nonlinear Schrödinger system in an optical fiber

Darboux transformation, bright and dark–bright solitons of an N-coupled high-order nonlinear Schrödinger system in an optical fiber

Bilinear form, solitons, breathers, lumps and hybrid solutions for a (3+1)-dimensional Date-Jimbo-Kashiwara-Miwa equation

Darboux transformation, bright and dark-bright solitons of an N-coupled high-order nonlinear Schrödinger system in an optical fiber

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