Matter-wave solitons in a spin-1 Bose-Einstein condensate with time-modulated external potential and scattering lengths

Wang, Deng‐Shan; Shi, Yu-Ren; Chow, K. W.; Yu, Zhao-Xian; Li, Xiang-Gui

doi:10.1140/epjd/e2013-40451-4

Cited by 15 publications

(7 citation statements)

References 27 publications

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“…For the case of = 2 we demonstrate some novel nonlinear structures by choosing the arbitrary function ( 1 + 2 + 0 + 3 ) specially. The separation transformation method may also be useful to solve other nonlinear wave models to explain the nonlinear excitations and localized nonlinear wave structures [19][20][21][22][23] in the physics of elementary particles and fields.…”

Section: Resultsmentioning

confidence: 99%

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Separation Transformation and a Class of Exact Solutions to the Higher-Dimensional Klein-Gordon-Zakharov Equation

Chen

Liu

Liu³

2014

Advances in Mathematical Physics

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The separation transformation method is extended to then+1-dimensional Klein-Gordon-Zakharov equation describing the interaction of the Langmuir wave and the ion acoustic wave in plasma. We first reduce then+1-dimensional Klein-Gordon-Zakharov equation to a set of partial differential equations and two nonlinear ordinary differential equations of the separation variables. Then the general solutions of the set of partial differential equations are given and the two nonlinear ordinary differential equations are solved by extendedF-expansion method. Finally, some new exact solutions of then+1-dimensional Klein-Gordon-Zakharov equation are proposed explicitly by combining the separation transformation with the exact solutions of the separation variables. It is shown that, for the case ofn≥2, there is an arbitrary function in every exact solution, which may reveal more nontrivial nonlinear structures in the high-dimensional Klein-Gordon-Zakharov equation.

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Section: Resultsmentioning

confidence: 99%

“…show particular nonlinear wave structures at time = 0, given by (33)-(34),(23), and (24) with (36) and the function selection ( ) = √ 2 + 1 demonstrates a particular nonlinear wave structure at time = 0, given by (33)-(34) and (24) with parameters in (36) and (38) and the function selection ( ) = sin ( + 1) .…”

mentioning

confidence: 98%

Separation Transformation and a Class of Exact Solutions to the Higher-Dimensional Klein-Gordon-Zakharov Equation

Chen

Liu

Liu³

2014

Advances in Mathematical Physics

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“…This is consistent with the real Bose-Einstein condensate experiments. There are indeed many papers [16][17][18][21][22][23][24][25][26][27][28]] studying the exact solutions of the nonlinear Schrödinger equations by similarity transformations, but they discuss either the matter-wave solitons of Bose-Einstein condensate with two-body interactions or the matterwave solitons of Bose-Einstein condensate with spatially Advances in Condensed Matter Physics 7 inhomogeneous interactions. To our knowledge, the three families of exact solutions (40)-(42) for the cubic-quintic nonlinear Schrödinger are proposed for the first time.…”

Section: Discussionmentioning

confidence: 99%

“…where Χ, , and are given by (6), (9), and (24) and functions 1 , 2 , 1 , 2 , 3 , and are given by (19)- (26). Here the value of function 1 is the key to the solution.…”

Section: Exact Matter-wave Soliton Solutions Of (1)mentioning

confidence: 99%

Dynamics and Matter-Wave Solitons in Bose-Einstein Condensates with Two- and Three-Body Interactions

Chen¹,

Yang²,

Zhang³

2014

Advances in Condensed Matter Physics

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By means of similarity transformation, this paper proposes the matter-wave soliton solutions and dynamics of the variable coefficient cubic-quintic nonlinear Schrödinger equation arising from Bose-Einstein condensates with time-dependent two- and three-body interactions. It is found that, under the effect of time-dependent two- and three-body interaction and harmonic potential with time-dependent frequency, the density of atom condensates will gradually diminish and finally collapse.

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“…In a dilute weakly interacting ultracold bose gas different type of solitons are formed due to the interplay between positive dispersion and positive or negative atom-atom interactions. In atomic BECs the formation of different type of solitons in different atom-atom interaction regime have been observed and also studied theoretically [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42].…”

Section: Introductionmentioning

confidence: 99%

Dynamics of atomic and molecular solitary waves inatom-molecular hybrid Bose-Einstein condensates coupled by Magnetic Feshbach Resonance: Role of induced decays of Feshbach Molecules

Dastidar,

Ray

2016

Preprint

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Dynamics of atomic and molecular bright solitons in a hybrid atom-molecular BEC (Bose Einstein Condensate) system of 85 Rb coupled through Magnetic Feshbach Resonance (MFR) has been investigated. By solving the time independent atom-molecular coupled equations, the initial atomic and molecular wavefunctions were obtained and the dynamics of the initial atomic and molecular waves in a spherical one-dimensional trap were studied by solving the time-dependent atom-molecular coupled equations. During evolution two types of induced or stimulated decays of the feshbach molecules were switched on. These two types of stimulated decays of the feshbach molecules (i) to the two-atom continuum and (ii) to the bound level of the lowest hyperfine state of the molecule were induced by laser/RF (Radio Frequency) fields. Hence the strength of these two induced decays can be controlled by varying the laser/RF field parameters e.g. intensity, detuning etc. It is found that depending on the relative strength of these two types of stimulated or induced decays initial atomic and molecular waves assume solitonic nature as bright solitons during evolution and the stability of these solitonic waves can be achieved by controlling the relative strength of induced decays in two different channels. It is shown that these two induced decays lead to the formation of stable atomic and molecular solitons by suppressing the initial oscillations and instability in the atom-molecular coupled system of 85 Rb atoms.

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Matter-wave solitons in a spin-1 Bose-Einstein condensate with time-modulated external potential and scattering lengths

Cited by 15 publications

References 27 publications

Separation Transformation and a Class of Exact Solutions to the Higher-Dimensional Klein-Gordon-Zakharov Equation

Separation Transformation and a Class of Exact Solutions to the Higher-Dimensional Klein-Gordon-Zakharov Equation

Dynamics and Matter-Wave Solitons in Bose-Einstein Condensates with Two- and Three-Body Interactions

Dynamics of atomic and molecular solitary waves inatom-molecular hybrid Bose-Einstein condensates coupled by Magnetic Feshbach Resonance: Role of induced decays of Feshbach Molecules

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