Abstract
In this paper, we investigate a five-component Gross–Pitaevskii equation, which is demonstrated to describe the dynamics of an F=2 spinor Bose–Einstein condensate in one dimension. By employing the Hirota method with an auxiliary function, we obtain the explicit bright one- and two-soliton solutions for the equation via symbolic computation. With the choice of polarization parameter and spin density, the one-soliton solutions are divided into four types: one-peak solitons in the ferromagnetic and cyclic states and one- and two-peak solitons in the polar states. For the former two, solitons share the similar shape of one peak in all components. Solitons in the polar states have the one- or two-peak profiles, and the separated distance between two peaks is inversely proportional to the value of polarization parameter. Based on the asymptotic analysis, we analyze the collisions between two solitons in the same and different states.
Highlights
E dynamics of nonlinear phenomena can be analyzed by means of the corresponding nonlinear evolution equations. ere has been considerable work carried out on the control problem of nonlinear systems, such as those in chaotic and stochastic systems [15,16,17,18,19]
In the spinor BECs, matter-wave solitons are thought to be useful for their application in the atom laser, atom interferometry, and coherent atom transport, which can contribute to the realization of quantum information processors or computation [26]. e dynamics of magnetic soliton, dark soliton, and dark-bright vector soliton in spinor Bose–Einstein condensates have been investigated [27,28,29,30]
We have investigated the solitons and their collisions for the five-component GP equations, i.e., equation (1), which can describe the dynamics of an F 2 spinor BECs in one dimension. rough the Hirota method and symbolic computation, we have derived one-soliton solutions (8) and two-soliton solutions (16) for equation (1)
Summary
E dynamics of nonlinear phenomena can be analyzed by means of the corresponding nonlinear evolution equations. ere has been considerable work carried out on the control problem of nonlinear systems, such as those in chaotic and stochastic systems [15,16,17,18,19]. E spinor BECs with spin F is described by a (2F + 1)-component mean-field wave function [31]. For equation (1), we will present the Hirota form with an auxiliary function and explicit one- and twosoliton solutions. In order to understand the dynamics of equation (1), it is essential to obtain the soliton solutions. E Hirota bilinear method is a tool to construct the soliton solutions for certain nonlinear evolution equations [36]. For equation (1), we will utilize the Hirota method with an auxiliary function to obtain the one- and two-soliton solutions. S ε2s2 + ε4s4 + ε6s6 + · · · , where ε is the formal parameter, g(±l)j’ s (l 1, 3, 5, · · ·) are the complex functions of t and x, and fm’s (m 2, 4, 6, · · ·) are the real ones which will be determined later
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