Xinhan Liu

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20232026

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math.AP2026

Local and global well-posedness for the nonlinear Schrödinger equation with nonhomogeneous boundary conditions

Engui Fan, Yuan Li, Xinhan Liu

In this paper, we study the initial-boundary value problem for the nonlinear Schrödinger equation in $R_{+}^{n}$ \begin{equation*} i\partial_{t}u+Δu+λ|u|^pu=0, \qquad (x,…

math.AP2024

$L^{2}$ -Sobolev space bijectivity and existence of global solutions for the matrix nonlinear Schrödinger equations

Yuan Li, Xinhan Liu, Engui Fan

We consider the Cauchy problem to the general defocusing and focusing $p \times q$ matrix nonlinear Schrödinger (NLS) equations with initial data allowing arbitrary-order poles and…

math.AP2023

Existence of global solutions for the nonlocal derivation nonlinear Schrödinger equation by the inverse scattering transform method

Yuan Li, Xinhan Liu, Engui Fan

We address the existence of global solutions to the initial value problem for the integrable nonlocal derivative nonlinear Schrödinger equation in weighted Sobolev space $H^{2}(\ma…

Local and global well-posedness for the nonlinear Schrödinger equation with nonhomogeneous boundary conditions

L2-Sobolev space bijectivity and existence of global solutions for the matrix nonlinear Schrödinger equations

Existence of global solutions for the nonlocal derivation nonlinear Schrödinger equation by the inverse scattering transform method

$L^{2}$ -Sobolev space bijectivity and existence of global solutions for the matrix nonlinear Schrödinger equations