On the integrability and isotopic structure of the one-dimensional Hubbard model in the long wave approximation

Makhankov, V.G.; Makhaldiani, Nugzar; Pashaev, Oktay K.

doi:10.1016/0375-9601(81)90051-7

Cited by 55 publications

(42 citation statements)

References 5 publications

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“…On the other case, δ = −1, the aforementioned system (2) is called the mixed CNLS (or modified Manakov model), which has attracted a lot of attention recently. The known solutions (say as brightbright, bright-dark, dark-dark type one-soliton solutions) and some new solutions of the mixed CNLS equation have been unearthed [4,7,11] and then singular and nonsingular bright multisoliton solutions have been obtained in [12]. In order to control boundary conditions at infinity, we impose the natural constraints [44] ξ → 0 at r → 0 , ξ → ∞ at r → ∞ .…”

Section: The Similarity Transformationmentioning

confidence: 99%

“…If simply setting µ = 1 and δ = −1, (2) becomes the mixed CNLS equation and the bright-dark soliton solutions of corresponding system can be expressed by the form [4,11] …”

Section: Bright-dark Solitonmentioning

confidence: 99%

“…In Figure 1c, if setting n j = 0, in which G j (t) change from a hyperbolic function to a trigonometric function, and the periodicities of them alter evidently, the amplitudes of the bright-dark soliton also yield the same periodic changes. For completeness, one can also select the bright-bright soltion solution, the dark-dark soltion solution or other type of solution to make some corresponding discussions [4,7,11,12].…”

Section: Bright-dark Solitonmentioning

confidence: 99%

See 2 more Smart Citations

Three-Dimensional Bright–Dark Soliton, Bright Soliton Pairs, and Rogue Wave of Coupled Nonlinear Schr¨odinger Equation with Time–Space Modulation

Chen

2012

Zeitschrift Für Naturforschung A

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We systematically provide a similarity transformation reducing the (3 + 1)-dimensional inhomogeneous coupled nonlinear Schrödinger (CNLS) equation with variable coefficients and parabolic potential to the (1 + 1)-dimensional coupled nonlinear Schrödinger equation with constant coefficients. Based on the similarity transformation, we discuss the dynamics of the propagation of the three-dimensional bright-dark soliton, the interaction between two bright solitons, and the feature of the three-dimensional rogue wave with different parameters. The obtained results may raise the possibility of relative experiments and potential applications.

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Section: The Similarity Transformationmentioning

confidence: 99%

“…If simply setting µ = 1 and δ = −1, (2) becomes the mixed CNLS equation and the bright-dark soliton solutions of corresponding system can be expressed by the form [4,11] …”

Section: Bright-dark Solitonmentioning

confidence: 99%

Section: Bright-dark Solitonmentioning

confidence: 99%

See 1 more Smart Citation

Three-Dimensional Bright–Dark Soliton, Bright Soliton Pairs, and Rogue Wave of Coupled Nonlinear Schr¨odinger Equation with Time–Space Modulation

Chen

2012

Zeitschrift Für Naturforschung A

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“…Such a subset is (a 2 , b 2 , p, q). First, the subsystem (14), (16), linear inhomogeneous in (a 2 , b 2 ), is solved on C as…”

Section: Leading Order Of Two Coupled Cgl3mentioning

confidence: 99%

“…In order to have an idea of the class of expressions among which to search for exact solutions, let us consider the integrable limit of our system, i. e. the unique case p real, q real, γ = 0 and, for two coupled equations, v = 0, δ = ±1 [15,16].…”

Section: Hints From the Integrable Limitmentioning

confidence: 99%

Analytic expressions of hydrothermal waves

Conte

Musette

2000

Reports on Mathematical Physics

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When subjected to a horizontal temperature difference, a fluid layer with a free surface becomes unstable and hydrothermal waves develop in the bulk. Such a system is modelized by two coupled amplitude equations of the one-dimensional, complex, cubic Ginzburg-Landau type. By transposing the method developed for one CGL3 equation, we obtain several new exact solutions expressed by closed form, singlevalued, analytic expressions. Some of them are the analogue of the famous amplitude hole solution of Bekki and Nozaki.

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Solitary Excitations in 1 ‐D Antiferromagnetic Systems with Finite Band Width

Lindner

1982

Physica Status Solidi (b)

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The experimental results in quasi 1-d antiferromagnets, e.g. TMMC, CPC /I/, which suggest non-linear effects, have been interpreted as yet in terms of the antiferromagnetic Heisenberg model.Here we consider a 1 -d model with finite band width, for which we have shown recently /2 to 4/ that in continuum approximation s o l i t a j solutions exist.2) We calculate the excitation energy, and in the way like Krumhansl and Schrieffer /5/ the free energy, the static correlation function of the lattice motion, and the width of the central peak of the dynamic structure factor connected with the solitary excitations.Formerly w e have shown /4/ that the model in time-dependent mean-field approximation and in continuum limit is given by the following Lagrangian density:* with t h e condition that (a/a t ) 1 ib= 0 at the boundary of the system. X_ is 0-the Hamiltonian density and for the other notations see /l/. (Instead o f t < 0 in /1/ w e write here -t . ) In continuum limit we have R.--+ a @ and u.(t) -+ ax(5,t). The upper signs in (1) concern the antiferromagnetic case, the lower signs the ferromagnetic one. In the following we restrict ourselves to the antiferromagnetic case. Instead of the complex probability amplitudes aO-(4, t ) and 10 J 1) Linnbstr. 5, DDR-7010 Leipzig, GDR.2 ) In /2/ instead of I in ( 1 9 ) p d (20) read -I and instead of (w2 -wo) in .(221, (24), (27), and (38) read (wo -w2).

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On the integrability and isotopic structure of the one-dimensional Hubbard model in the long wave approximation

Cited by 55 publications

References 5 publications

Three-Dimensional Bright–Dark Soliton, Bright Soliton Pairs, and Rogue Wave of Coupled Nonlinear Schr¨odinger Equation with Time–Space Modulation

Three-Dimensional Bright–Dark Soliton, Bright Soliton Pairs, and Rogue Wave of Coupled Nonlinear Schr¨odinger Equation with Time–Space Modulation

Analytic expressions of hydrothermal waves

Solitary Excitations in 1 ‐D Antiferromagnetic Systems with Finite Band Width

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