Xinhan Liu

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20242026

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math.AP2026

Local and global well-posedness for the nonlinear SchrÃ¶dinger equation with nonhomogeneous boundary conditions

Engui Fan, Yuan Li, Xinhan Liu

In this paper, we study the initial-boundary value problem for the nonlinear SchrÃ¶dinger equation in $R_{+}^{n}$ \begin{equation*} i\partial_{t}u+Îu+Î»|u|^pu=0, \qquad (…

math.AP2024

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

Yuan Li, Xinhan Liu, Engui Fan

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

Local and global well-posedness for the nonlinear SchrÃ¶dinger equation with nonhomogeneous boundary conditions

L2-Sobolev space bijectivity and existence of global solutions for the matrix nonlinear SchrÃ¶dinger equations

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