Self-similar solutions to the derivative nonlinear Schrödinger equation

Abstract

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.

arXiv comment16 pages, no figures

References in corpus (2)

• On the Cauchy problem for the derivative nonlinear Schroedinger equation with periodic boundary condition
• Global well-posedness on the derivative nonlinear Schrödinger equation revisited

Cited by in corpus (1)

• On the well-posedness problem for the derivative nonlinear Schrödinger equation