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Two accelerated imaginary-time evolution methods are proposed for thecomputation of solitary waves in arbitrary spatial dimensions. For the firstmethod (with traditional power normalization), the convergence conditions aswell as conditions for optimal accelerations are derived. In addition, it isshown that for nodeless solitary waves, this method converges if and only ifthe solitary wave is linearly stable. The second method is similar to the firstmethod except that it uses a novel amplitude normalization. The performance ofthese methods is illustrated on various examples. It is found that while thefirst method is competitive with the Petviashvili method, the second methoddelivers much better performance than the first method and the Petviashvilimethod.

Accelerated Imaginary-time Evolution Methods for the Computation of Solitary Waves