Differential and Integral Equations

The stochastic derivative nonlinear Schrödinger equation

Sijia Zhong

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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

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

First available in Project Euclid: 20 January 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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]


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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