We present analytical solution, which is periodic in nature, for a driven cubic–quartic nonlinear Schrödinger equation (DCQNLSE) is placed in a bi-chromatic optical lattice. The solution indicates the creation of density wave. Since, beyond mean-field contribution in quasi one dimensional and one dimensional geometry differs on the even exponents of the nonlinearity thus we extend our analysis toward quadratic–cubic–quartic and quadratic–cubic nonlinearities as well. Later, we study the dynamics of DCQNLSE. Our study indicates the existence of stripe phase along with considerable phase coherence. These findings allow us to comment on the possible emergence of supersolid phase in a condensate.

中文翻译：

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受驱动的三次-四次非线性薛定谔方程中的超固体特征

我们提出了本质上是周期性的解析解，用于将驱动的三次四次非线性薛定谔方程 (DCQNLSE) 置于双色光学晶格中。该解决方案表明密度波的产生。由于除了准一维和一维几何中的平均场贡献之外，非线性的偶数指数也不同，因此我们也将分析扩展到二次-三次-四次和二次-三次非线性。稍后，我们研究 DCQNLSE 的动力学。我们的研究表明存在条纹相以及相当大的相位相干性。这些发现使我们能够评论凝聚态中可能出现的超固相。