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Abstract:We develop a unified methodology that integrates spectral theory, Riemann-Hilbert problems, and inverse scattering theory for the construction and numerical evaluation of transform pairs associated with linear variable-coefficient partial differential equations. The approach combines analytical formulae with numerical methods for ordinary differential equations and Riemann-Hilbert problems, yielding a hybrid analytical-numerical strategy for working with these transforms. Results are presented for transforms arising in the Dirac equation, demonstrating accurate computations, even in the presence of discontinuous coefficients.
From: Kaitlynn Lilly [view email]
[v1]
Wed, 24 Jun 2026 00:17:04 UTC (938 KB)
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