School of Mathematics and Systematic Sciences, Shenyang Normal University, Shenyang, 110034, China.
Sci Rep. 2017 Sep 6;7(1):10638. doi: 10.1038/s41598-017-10205-4.
We investigate non-autonomous multi-rogue wave solutions in a three-component(spin-1) coupled nonlinear Gross-Pitaevskii(GP) equation with varying dispersions, higher nonlinearities, gain/loss and external potentials. The similarity transformation allows us to relate certain class of multi-rogue wave solutions of the spin-1 coupled nonlinear GP equation to the solutions of integrable coupled nonlinear Schrödinger(CNLS) equation. We study the effect of time-dependent quadratic potential on the profile and dynamic of non-autonomous rogue waves. With certain requirement on the backgrounds, some non-autonomous multi-rogue wave solutions exhibit the different shapes with two peaks and dip in bright-dark rogue waves. Then, the managements with external potential and dynamic behaviors of these solutions are investigated analytically. The results could be of interest in such diverse fields as Bose-Einstein condensates, nonlinear fibers and super-fluids.
我们研究了一个具有变色散、高阶非线性、增益/损耗和外势的三分量（自旋-1）耦合非线性 Gross-Pitaevskii（GP）方程中的非自治多孤子波解。相似变换使我们能够将自旋-1 耦合非线性 GP 方程的某些类多孤子波解与可积耦合非线性薛定谔（CNLS）方程的解联系起来。我们研究了时变二次势对非自治孤子波轮廓和动力学的影响。在一定的背景要求下，某些非自治多孤子波解表现出不同形状的亮暗孤子波，具有双峰和凹陷。然后，对这些解的外势控制和动力学行为进行了分析。这些结果可能在玻色-爱因斯坦凝聚、非线性光纤和超流等多个领域中具有重要意义。
