On the construction of Beltrami fields and associated boundary value problems

PDEs in connection with optics and electromagnetic theory (35Q60) Functions of hypercomplex variables and generalized variables (30G35) Transform methods (e.g., integral transforms) applied to PDEs (35A22) Linear first-order PDEs (35F05) General theory of PDEs and systems of PDEs with constant coefficients (35E20) PDEs in connection with astronomy and astrophysics (35Q85)

Cites Work

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Transmutations, \(L\)-bases and complete families of solutions of the stationary Schrödinger equation in the plane
Transmutations d'opérateurs différentiels dans le domaine complexe
Sturm-Liouville operators and applications. Transl. from the Russian by A. Iacob
A boundary integral equation method for a Neumann boundary problem for force-free fields
Representation of solutions to the one-dimensional Schrödinger equation in terms of Neumann series of Bessel functions
Complete systems of Beltrami fields using complex quaternions and transmutation theory
Reduced-quaternionic Mathieu functions, time-dependent Moisil-Teodorescu operators, and the imaginary-time wave equation
Transmutations, singular and fractional differential equations with applications to mathematical physics
A right inverse operator for \(\operatorname{curl}+\lambda \) and applications
Transmutations for Darboux transformed operators with applications
A representation for solutions of the Sturm–Liouville equation
The treatment of a Neumann boundary value problem for force-free fields by an integral equation method
On the linear force-free fields in bounded and unbounded three-dimensional domains
Methods of Mathematical Physics
Direct and Inverse Sturm-Liouville Problems
Spectral parameter power series for Sturm–Liouville problems
Biquaternionic treatment of inhomogeneous time-harmonic Maxwell's equations over unbounded domains
A right inverse of curl which is divergence‐free invariant and some applications to generalized Vekua‐type problems

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