7 papers
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 \begin{equation*} i\partial_{t}u+Δu+λ|u|^pu=0, \qquad (x,…
Flow Subgraphs and Flow Network Design under End-to-End Power Dissipation Constraints
Zhihao Qiu, Xinhan Liu, Rogier Noldus +1
We investigate how the underlying graph of a network supports a flow between a source node and a destination node and propose to compute the expected number of nodes and links that…
Geometric Organization and Inference of Shortest Path Nodes in Soft Random Geometric Graphs
Zhihao Qiu, Sámuel G. Balogh, Xinhan Liu +2
The shortest path problem is related to many dynamic processes on networks, ranging from routing in communication networks to signaling in molecular interaction networks. When the…
Corrigendum to "Degree-Based Approximations for Network Reliability Polynomials". Comment on J. Complex Networks 2025, 13, cnaf001
Xinhan Liu, Piet Van Mieghem
Our original paper \cite{VanMieghem2025} described the stochastic approximation in \cite[eq. (2.2)]{VanMieghem2025} and the first-o…
Node Reliability: Approximation, Upper Bounds, and Applications to Network Robustness
Xinhan Liu, Robert Kooij, Piet Van Mieghem
This paper discusses the reliability of a graph in which the links are perfectly reliable but the nodes may fail with certain probability p. Calculating graph node reliability is a…
-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 matrix nonlinear Schrödinger (NLS) equations with initial data allowing arbitrary-order poles and…
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…