Generation of matter-wave solitons of the Gross-Pitaevskii equation with a time-dependent complicated potential

Three-Body Interactions Beyond the Gross–pitaevskii Equation and Modulational Instability of Bose–einstein Condensates

“…(4). First, we transform the wavefunction q(x, t) by using the following modified lens-type transformation [16][17][18][19] q(x, t) = 1…”

“…(27) reduces to the solution obtained above when the free parameters take the following values: C 5 = 1, and t 0 = 0. In the previous works,4,11,[17][18][19]22 the case where the external potential is turned off cannot be investigated analytically, since the solution of the Riccati equation1250202-11 Int. J. Mod.…”

Modulational Instability of a Bose–einstein Condensate Beyond the Fermi Pseudopotential With a Time-Dependent Complex Potential

“…[1][2][3] After the production of condensates, many experimental and theoretical works have been devoted to the investigation of the BECs properties such as dark solitons, 4-9 bright solitons, 10,11 the generation and evolution of coherent structures via the MI [12][13][14][15][16][17] and so on. The phenomenon of MI is a general feature that appears in many nonlinear systems as a result of an interplay between the nonlinear and the dispersive effects and was studied during the 1960s in diverse fields, such as fluid dynamics, nonlinear optics and plasma physics.…”

“…The phenomenon of MI is a general feature that appears in many nonlinear systems as a result of an interplay between the nonlinear and the dispersive effects and was studied during the 1960s in diverse fields, such as fluid dynamics, nonlinear optics and plasma physics. 18 Recently, the phenomenon of MI was reported in the context of BECs both in experimental and theoretical works, [12][13][14][15][16][17][19][20][21][22] and it has been considered as being responsible for dephasing and localization phenomena in BECs. [12][13][14][15][16][17]21,22 Condensate gases of very dilute alkali atomic species are well described by the mean-field Gross-Pitaevskii equation (GPE) for the condensate wavefunction.…”

“…35 The generation and propagation of matter-wave solitons in BECs via the MI have been paid increasing interests in the recent past years. [12][13][14][15][16][17][21][22][23][24] Most of the previous works devoted to study the MI in condensates do not take into account neither the effects of quantum fluctuations nor the effects of the shape-dependent correction term, on the MI process in condensates. However, Tiofack et al 36 have just considered the latter effects on the MI of cigar-shaped BECs confined in an external harmonic potential trap.…”