Focusing Singularity in a Derivative Nonlinear Schr\"odinger Equation

Xiao Liu; Gideon Simpson; Catherine Sulem

doi:10.48550/arxiv.1301.1048

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$Focusing Singularity in a Derivative Nonlinear Schr\"odinger Equation$

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Focusing Singularity in a Derivative Nonlinear Schr\"odinger Equation

Xiao Liu, Gideon Simpson and Catherine Sulem

06 Jan 2013

DOI: https://doi.org/10.48550/arxiv.1301.1048

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Abstract

Mathematics - Analysis of PDEs

We present a numerical study of a derivative nonlinear Schr\"odinger equation with a general power nonlinearity, $|\psi|^{2\sigma}\psi_x$. In the $L^2$-supercritical regime, $\sigma>1$, our simulations indicate that there is a finite time singularity. We obtain a precise description of the local structure of the solution in terms of blowup rate and asymptotic profile, in a form similar to that of the nonlinear Schr\"odinger equation with supercritical power law nonlinearity.

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Title: Focusing Singularity in a Derivative Nonlinear Schr\"odinger Equation
Creators: Xiao Liu
Gideon Simpson
Catherine Sulem
Resource Type: Preprint
Language: English
Academic Unit: Mathematics
Other Identifier: 991019296796704721

Focusing Singularity in a Derivative Nonlinear Schr\"odinger Equation

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