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A deep learning improved numerical method for the simulation of rogue waves of nonlinear Schrodinger equation

机译:深度学习改进了非线性薛定林方程的流氓波模拟数值方法

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Modulation instability (MI) is a pervasive phenomenon in nonlinear science. It is inevitable for simulating rogue wave or breather solutions of the focusing nonlinear Schr & ouml;dinger equation (NLSE) and other application problems with MI involved. Due to MI, the small perturbation on the boundary can lead to large and non-negligible errors for the simulation of initial-boundary problems. To deal with this challenging problem, we propose a method to modify the boundary problem through a deep learning algorithm so that the long time simulation for the rogue wave or breather solutions to the NLSE can be performed with a superior numerical errors. We impose different types of rogue wave and breather solutions for the focusing NLSE as initial data to test the proposed method. It turns out that the proposed method gives rise to the better numerical results in compared with the ones obtained by traditional methods, which paves a way to simulate other physical problems with MI. (c) 2021 Elsevier B.V. All rights reserved.
机译:调制不稳定(MI)是非线性科学的普遍存存现象。模拟聚焦非线性Schr&Ouml的流氓波或呼吸解决方案是不可避免的; Dinger方程(NLSE)和涉及MI的其他应用问题。由于MI,对边界的小扰动可能导致初始边界问题的模拟的大而不可忽略的误差。为了处理这一具有挑战性的问题,我们提出了一种通过深度学习算法修改边界问题的方法,使得可以使用优异的数值误差来执行对NLSE的恶意波或呼吸器解决方案的长时间仿真。我们对聚焦NLSE的初始数据强加不同类型的流氓波和呼吸解决方案以测试所提出的方法。事实证明,与通过传统方法获得的那些,所提出的方法引起了更好的数值结果,该方法铺平了一种方法来模拟MI的其他身体问题。 (c)2021 elestvier b.v.保留所有权利。

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