Differential and Integral Equations

The stochastic derivative nonlinear Schrödinger equation

Sijia Zhong

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Abstract

In this paper, we will use a gauge transform to prove the local existence and uniqueness of the derivative nonlinear Schrödinger equation with additive noise, showing that for the initial data $u_0\in H^\frac{1}{2}(\mathbb{R})$, there is a local and unique solution almost surely.

Article information

Source
Differential Integral Equations, Volume 30, Number 1/2 (2017), 81-100.

Dates
First available in Project Euclid: 20 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.die/1484881220

Mathematical Reviews number (MathSciNet)
MR3599796

Zentralblatt MATH identifier
06738542

Subjects
Primary: 60H15: Stochastic partial differential equations [See also 35R60] 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10] 35R60: Partial differential equations with randomness, stochastic partial differential equations [See also 60H15]

Citation

Zhong, Sijia. The stochastic derivative nonlinear Schrödinger equation. Differential Integral Equations 30 (2017), no. 1/2, 81--100. https://projecteuclid.org/euclid.die/1484881220


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