Computing stationary solutions of the two-dimensional Gross-Pitaevskii equation with deflated continuation
Computing stationary solutions of the two-dimensional Gross-Pitaevskii equation with deflated continuation
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DOI：
10.1016/j.cnsns.2017.05.024
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发表时间：
2018-01-01
影响因子：
3.9
通讯作者：
Farrell, P. E.
中科院分区：
文献类型：
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作者：
Charalampidis, E. G.;Kevrekidis, P. G.;Farrell, P. E.
在这项工作中，我们采用了最近提出的分岔分析技术，即deflated延延算法，来计算具有抛物陷阱和排斥相互作用的单分量二维非线性薛定谔方程中的稳态孤立波形。尽管该系统已被广泛研究，但我们发现了各种各样以前未知的解决方案分支。我们分析了新发现的分支的稳定性，并讨论了它们在近线性（笛卡尔和极）和高度非线性情况下与已知解相关的分支。虽然压缩延拓不能保证计算出完整的分岔图，但这一分析有力地证明了该算法可以发现新的非线性状态，并为复杂高维哈密顿动力系统的能量格局提供见解。(C) 2017年作者。这是一篇基于CC by许可的开放获取文章。
In this work we employ a recently proposed bifurcation analysis technique, the deflated continuation algorithm, to compute steady-state solitary waveforms in a one-component, two-dimensional nonlinear Schrodinger equation with a parabolic trap and repulsive interactions. Despite the fact that this system has been studied extensively, we discover a wide variety of previously unknown branches of solutions. We analyze the stability of the newly discovered branches and discuss the bifurcations that relate them to known solutions both in the near linear (Cartesian, as well as polar) and in the highly nonlinear regimes. While deflated continuation is not guaranteed to compute the full bifurcation diagram, this analysis is a potent demonstration that the algorithm can discover new nonlinear states and provide insights into the energy landscape of complex high-dimensional Hamiltonian dynamical systems. (C) 2017 The Authors. Published by Elsevier B. V. This is an open access article under the CC BY license.