TY - JOUR
T1 - Self-similar solutions to the derivative nonlinear Schrödinger equation
AU - Fujiwara, Kazumasa
AU - Georgiev, Vladimir
AU - Ozawa, Tohru
N1 - Funding Information:
The first author was supported in part by Grant-in-Aid for JSPS Fellows Number 201900334.The second author was supported in part by Project 2017 ?Problemi stazionari e di evoluzione nelle equazioni di campo nonlineari? of INDAM, GNAMPA - Gruppo Nazionale per l'Analisi Matematica, la Probabilit? e le loro Applicazioni, by Institute of Mathematics and Informatics, Bulgarian Academy of Sciences and Top Global University Project, Waseda University, by the University of Pisa, Project PRA 2018 49 and project ?Dinamica di equazioni nonlineari dispersive?, ?Fondazione di Sardegna?, 2016.
Publisher Copyright:
© 2019 Elsevier Inc.
PY - 2020/6/5
Y1 - 2020/6/5
N2 - A class of self-similar solutions to the derivative nonlinear Schrödinger 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.
AB - A class of self-similar solutions to the derivative nonlinear Schrödinger 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.
KW - Derivative nonlinear Schrödinger equations
KW - Self-similar solution
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U2 - 10.1016/j.jde.2019.11.089
DO - 10.1016/j.jde.2019.11.089
M3 - Article
AN - SCOPUS:85081654699
SN - 0022-0396
VL - 268
SP - 7940
EP - 7961
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 12
ER -