arXiv subjects

Laila S. Busaleh

Publications and source records attributed to Laila S. Busaleh.

3 recordsLinked to original sources

arXiv2026

Homogenized Equations for Isentropic Gas in a Pipe with Periodically-Varying Cross-Section

We analyze the behavior of an isentropic gas in a narrow pipe with periodically-varying cross-sectional area. Using multiple-scale perturbation theory, we derive homogenized effective equations, which take the form of a constant-coefficient system of evolution equations, including dispersive higher-order derivative terms. We provide an approximate Riemann solver for the variable-cross-section isentropic gas equations, and compare numerical solutions of the original system with those of the homogenized system. We observe that the resulting solutions take the form of solitary waves, rather than shock waves, under fairly general conditions.

math.AP↗

arXiv2026

Mitigating Barren Plateaus via Domain Decomposition in Variational Quantum Algorithms for Nonlinear PDEs

Barren plateaus present a major challenge in the training of variational quantum algorithms (VQAs), particularly for large-scale discretizations of nonlinear partial differential equations. In this work, we introduce a domain decomposition framework to mitigate barren plateaus by localizing the cost functional. Our strategy is based on partitioning the spatial domain into overlapping subdomains, each associated with a localized parameterized quantum circuit and measurement operator. Numerical results for the time-independent Gross-Pitaevskii equation show that the domain-decomposed formulation, allowing subdomain iterations to be interleaved with optimization iterations, exhibits improved solution accuracy and stable optimization compared to the global VQA formulation.

math.NA↗

arXiv2025

A Hyperbolic Approximation of the Nonlinear Schrödinger Equation

We study a first-order hyperbolic approximation of the nonlinear Schrödinger (NLS) equation. We show that the system is strictly hyperbolic and possesses a modified Hamiltonian structure, along with at least three conserved quantities that approximate those of NLS. We provide families of explicit standing-wave solutions to the hyperbolic system, which are shown to converge uniformly to ground-state solutions of NLS in the relaxation limit. The system is formally equivalent to NLS in the relaxation limit, and we develop asymptotic preserving discretizations that tend to a consistent discretization of NLS in that limit, while also conserving mass. Examples for both the focusing and defocusing regimes demonstrate that the numerical discretization provides an accurate approximation of the NLS solution.

math.AP↗