Pattern formations in miscellaneous mixtures of Bose-Einstein condensates and the higher-dimensional time-gated Manakov system

Kuetche, Victor K.; Bouetou, Thomas B.; Kofané, Timoléon Crépin; Moubissi, A. B.; Porsezian, K.

doi:10.1103/physreva.82.053619

Cited by 17 publications

(11 citation statements)

References 161 publications

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“…For the system to pass the P-analysis, three resonance conditions at j = 1, 2, and 3 are required such that three arbitrary functions among B j and C j can be introduced into the general series expansion given by Eq. (28).…”

Section: Painlevé-analysismentioning

confidence: 99%

“…(56) and (57) shows that in order to unearth the Hirota's bilinearization 21 of the aforementioned system, we can truncate the P-expansions (28) to the zeroth-order of the perturbative parameter . Thus, we define three arbitrary functions G, H , and F, such that…”

Section: Bäcklund Transformation and Hirota's Bilinearizationmentioning

confidence: 99%

“…Such an issue was previously carried out by Tang and Lou 71 through an "extended multilinear variable separation approach" for some (2 + 1)dimensional integrable systems while generating a family of diverse pattern formations by using arbitrary functions h derived from the Painlevé-analysis. According to the usual procedure of P-analysis, [25][26][27][28] observables A and C are computed by means of Eqs. (28) and (30) up to a zerothorder of the arbitrary singularity manifold h (see Eq.…”

Section: Pattern Formations With Fractal Backgroundsmentioning

confidence: 99%

“…According to the usual procedure of P-analysis, [25][26][27][28] observables A and C are computed by means of Eqs. (28) and (30) up to a zerothorder of the arbitrary singularity manifold h (see Eq. (54)) given by 71…”

Section: Pattern Formations With Fractal Backgroundsmentioning

confidence: 99%

See 3 more Smart Citations

Fractal structure of ferromagnets: The singularity structure analysis

Kuetche

Bouetou

Kofané

2011

Journal of Mathematical Physics

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Following the Weiss-Tabor-Carnevale approach [J. Weiss, M. Tabor, and G. Carnevale, J. Math. Phys. 24, 522 (1983); J. Weiss, M. Tabor, and G. Carnevale, J. Math. Phys. 25, 13 (1984).] designed for studying the integrability properties of nonlinear partial differential equations, we investigate the singularity structure of a (2 + 1)-dimensional wave-equation describing the propagation of polariton solitary waves in a ferromagnetic slab. As a result, we show that, out of any damping instability, the system above is integrable. Looking forward to unveiling its complete integrability, we derive its Bäcklund transformation and Hirota's bilinearization useful in generating a set of soliton solutions. In the wake of such results, using the arbitrary functions to enter into the Laurent series of solutions to the above system, we discuss some typical class of excitations generated from the previous solutions in account of a classification based upon the different expressions of a generic lower dimensional function. Accordingly, we unearth the nonlocal excitations of lowest amplitudes, the dromion and lump patterns of higher amplitudes, and finally the stochastic pattern formations of highest amplitudes, which arguably endow the aforementioned system with the fractal properties. C 2011 American Institute of Physics.

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Section: Painlevé-analysismentioning

confidence: 99%

Section: Bäcklund Transformation and Hirota's Bilinearizationmentioning

confidence: 99%

Section: Pattern Formations With Fractal Backgroundsmentioning

confidence: 99%

Section: Pattern Formations With Fractal Backgroundsmentioning

confidence: 99%

See 2 more Smart Citations

Fractal structure of ferromagnets: The singularity structure analysis

Kuetche

Bouetou

Kofané

2011

Journal of Mathematical Physics

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“…Moreover, the (1 + 1)-dimensional CNLS equation with varying coefficients have been investigated by means of different techniques in the literatures [25,26]. For the higher-dimensional case, very recently, Kuetche et al proved the complete integrability of the (2 + 1)-dimensional mixed CNLS equation (or modified Manakov model) by the Painlevé properties and the generalized Lax representation [27]. However, the realization of a higher-dimensional CNLS is still a challengeable topic for that adding a dimension may changes drastically the integrability properties of the equation.…”

Section: Introductionmentioning

confidence: 99%

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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General Lax-representation of a new higher-dimensional system: The current-fed membrane

Kuetche

2014

Chaos, Solitons & Fractals

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Pattern formations in miscellaneous mixtures of Bose-Einstein condensates and the higher-dimensional time-gated Manakov system

Cited by 17 publications

References 161 publications

Fractal structure of ferromagnets: The singularity structure analysis

Fractal structure of ferromagnets: The singularity structure analysis

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

General Lax-representation of a new higher-dimensional system: The current-fed membrane

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