A counterexample to the uniqueness result of Cox and Thompson
A.G. Ramm
TL;DR
This paper presents a counterexample that challenges the previously claimed uniqueness result in a 1970 inverse scattering problem paper by Cox and Thompson.
Contribution
It provides a specific counterexample demonstrating that the earlier proven uniqueness result does not hold universally.
Findings
Counterexample disproves the previous uniqueness claim
Challenges established assumptions in inverse scattering theory
Highlights need for revised conditions in uniqueness proofs
Abstract
A counterexample is given to the uniqueness result given in the paper by J.Cox and K.Thompson, "Note on the uniqueness of the solution of an equation of interest in inverse scattering problem", J. Math.Phys., 11, N3, (1970), 815-817.
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Taxonomy
TopicsNumerical methods in inverse problems · Advanced Mathematical Modeling in Engineering · Stability and Controllability of Differential Equations