Sun Wen-Rong, Wang Lei
School of Mathematics and Physics, Composite and Interface Science, University of Science and Technology Beijing, Beijing 100083, People's Republic of China.
Beijing Key Laboratory for Magneto-Photoelectrical, Composite and Interface Science, University of Science and Technology Beijing, Beijing 100083, People's Republic of China.
Proc Math Phys Eng Sci. 2018 Jan;474(2209):20170276. doi: 10.1098/rspa.2017.0276. Epub 2018 Jan 3.
To show the existence and properties of matter rogue waves in an =1 spinor Bose-Einstein condensate (BEC), we work on the three-component Gross-Pitaevskii (GP) equations. Via the Darboux-dressing transformation, we obtain a family of rational solutions describing the extreme events, i.e. rogue waves. This family of solutions includes bright-dark-bright and bright-bright-bright rogue waves. The algebraic construction depends on Lax matrices and their Jordan form. The conditions for the existence of rogue wave solutions in an =1 spinor BEC are discussed. For the three-component GP equations, if there is modulation instability, it is of baseband type only, confirming our analytic conditions. The energy transfers between the waves are discussed.
为了展示在(n = 1)的自旋玻色 - 爱因斯坦凝聚体（BEC）中物质 rogue 波的存在及其性质，我们研究了三分量的格罗斯 - 皮塔耶夫斯基（GP）方程。通过达布变换，我们得到了一族描述极端事件即 rogue 波的有理解。这族解包括亮 - 暗 - 亮和亮 - 亮 - 亮 rogue 波。代数构造依赖于拉克斯矩阵及其约当形式。讨论了(n = 1)自旋 BEC 中 rogue 波解存在的条件。对于三分量 GP 方程，如果存在调制不稳定性，它仅为基带类型，这证实了我们的解析条件。还讨论了波之间的能量转移。
