2021
DOI: 10.1142/9789814713955_0014
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History of Mathematics in American Mathematical Textbooks of the Late 19th and Early 20th Centuries

Abstract: The logarithmic Schrödinger equation (LogSE) has a logarithmic nonlinearity f (u) = u ln |u| 2 that is not differentiable at u = 0. Compared with its counterpart with a regular nonlinear term, it possesses richer and unusual dynamics, though the low regularity of the nonlinearity brings about significant challenges in both analysis and computation. Among very limited numerical studies, the semi-implicit regularized method via regularising f (u) as u ε ln(ε+|u ε |) 2 to overcome the blowup of ln |u| 2 at u = 0 … Show more

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References 91 publications
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