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.

Self-similar solutions to the derivative nonlinear Schrodinger equation

Gueorguiev, Vladimir Simeonov;Fujiwara, Kazumasa;
2020-01-01

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.
2020
Gueorguiev, Vladimir Simeonov; Fujiwara, Kazumasa; Ozawa, Tohru
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/1055322
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