Huygens' Principle,Dirac Operators,and Rational Solutions of the AKNS Hierarchy |
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Authors: | Email author" target="_blank">Fabio?A?C?C?ChalubEmail author Jorge?P?Zubelli |
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Institution: | (1) IMPA, Est. D. Castorina 110, RJ, 22460-320, Brazil |
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Abstract: | We prove that rational solutions of the AKNS hierarchy of the form q=σ/τ and r=ρ/τ, where (σ,τ,ρ) are certain Schur functions, naturally yield Dirac operators of strict Huygens' type, i.e., the support
of their fundamental solutions is the surface of the light-cone. This strengthens the connection between the theory of completely
integrable systems and Huygens' principle by extending to the Dirac operators and the rational solutions of the AKNS hierarchy
a classical result of Lagnese and Stellmacher concerning perturbations of wave operators.
Mathematics Subject Classifications (2000) 37K10, 35Qxx, 35B40. |
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Keywords: | Dirac operators fundamental solutions Huygens' principle integrable hierarchies rational solutions |
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