Accelerated Imaginary-time Evolution Methods for the Computation of Solitary Waves
Abstract
Two accelerated imaginary-time evolution methods are proposed for the computation of solitary waves in arbitrary spatial dimensions. For the first method (with traditional power normalization), the convergence conditions as well as conditions for optimal accelerations are derived. In addition, it is shown that for nodeless solitary waves, this method converges if and only if the solitary wave is linearly stable. The second method is similar to the first method except that it uses a novel amplitude normalization. The performance of these methods is illustrated on various examples. It is found that while the first method is competitive with the Petviashvili method, the second method delivers much better performance than the first method and the Petviashvili method.
Cite
@article{arxiv.0711.3434,
title = {Accelerated Imaginary-time Evolution Methods for the Computation of Solitary Waves},
author = {Jianke Yang and Taras I. Lakoba},
journal= {arXiv preprint arXiv:0711.3434},
year = {2007}
}
Comments
To appear in Stud. Appl. Math. (28 pages, 6 figures)