Highlights'/> Solitons in multi-body interactions for a fully modulated cubic-quintic Gross-Pitaevskii equation
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Solitons in multi-body interactions for a fully modulated cubic-quintic Gross-Pitaevskii equation

机译：完全调制的立方五次方Gross-Pitaevskii方程在多体相互作用中的孤子

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Highlights•Dynamics of solitons in a fully modulated cubic–quintic Gross–Pitaevskii equation is analyzed.•Role of quintic parameter on the size of wave numbers of carrier and envelope is analyzed.•Lax-pair for the model with varying coefficients and external potential is given.•Regions of modulational instability and linear and nonlinear stabilities are investigated.AbstractA phase imprint approach is applied to a cubic Gross–Pitaevskii equation (GPE) in order to obtain a modified non-autonomous derivative cubic–quintic nonlinear GPE with fully variable coefficients. This model describes the dynamics of condensates in Bose–Einstein condensates, with both two- and three-body interatomic interactions with an external potential when the coefficient of the dispersion term is constant. This model is also applicable to fiber optics media in the absence of external potential. We show that this modified GPE model has a Lax-pair when all of its coefficients depend on time. However, the external potential depends on both the time and space variables. We obtain two classes of exact analytical solutions. These classes of solutions contain four different types of solitary-like wave solutions in the form of kink, anti-kink, bright, dark solitary, and periodic wave solutions. We reveal the effects of a quintic term on wave numbers, for both the carrier and envelope waves. Stability analysis is carried out, and conditions on parameters that determine regions with linear stability are discussed. Graphical analysis of some solutions are presented.
机译： 突出显示 • 分析了完全调制的立方-五阶Gross-Pitaevskii方程中的孤子动力学。 • 五次参数对载波和包络波数大小的作用 • 给出了具有不同系数和外部电势的模型的松弛对。 • 研究了调制不稳定性以及线性和非线性稳定性的区域。 摘要 获得具有完全可变系数的修正的非自治微分三次方非线性GPE。该模型描述了当分散项的系数恒定时，玻色-爱因斯坦凝聚物中的凝聚物的动力学，其中两体和三体原子间相互作用以及外部电势。在没有外部电势的情况下，该模型也适用于光纤介质。我们表明，当修改后的GPE模型的所有系数都取决于时间时，它具有Lax对。但是，外部电势取决于时间和空间变量。我们获得两类精确的解析解。这些类型的解决方案包含四种不同类型的类孤波解决方案，包括扭结，抗扭结，亮，暗孤立和周期波解决方案。我们揭示了载波和包络波的五次项对波数的影响。进行了稳定性分析，并讨论了确定具有线性稳定性的区域的参数条件。给出了一些解决方案的图形分析。

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