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arXiv · 1811.06141

Self-similar solutions to the derivative nonlinear Schr\"odinger equation

Kazumasa Fujiwara·Vladimir Georgiev·Tohru Ozawa
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Abstract

A class of self-similar solutions to the derivative nonlinear Schr\"odinger equations is studied. Especially, the asymptotics of profile functions are shown to posses a logarithmic phase correction. This logarithmic phase correction is obtained from the nonlinear interaction of profile functions. This is a remarkable difference from the pseudo-conformally invariant case, where the logarithmic correction comes from the linear part of the equations of the profile functions.

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Kazumasa Fujiwara, Vladimir Georgiev, Tohru Ozawa. 2018-11-15. Self-similar solutions to the derivative nonlinear Schr\"odinger equation. https://arxiv.org/abs/1811.06141

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