Self-similar solutions to the derivative nonlinear Schrödinger equation. (English) Zbl 1435.35345
Summary: 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.
MSC:
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
| 35C06 | Self-similar solutions to PDEs |
| 35B40 | Asymptotic behavior of solutions to PDEs |
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