According to a theorem of Treves, the conserved functionals of the Ablowitz-Kaup-Newell-Segur (AKNS) equation vanish on all pairs of formal Laurent series of a specified form, both of them with a pole of the first order. We propose a new and very simple proof for this statement, based on the theory of Baecklund transformations; using the same method, we prove that the AKNS conserved functionals vanish on other pairs of Laurent series. The spirit is the same of our previous paper on the Treves theorem for the KdV equation (J.Math.Phys. 45 (2004) 3558-3564), with some non trivial technical differences.
On the Treves theorem for the Ablowitz-Kaup-Newell-Segur equation
MOROSI, CARLO;
2004-01-01
Abstract
According to a theorem of Treves, the conserved functionals of the Ablowitz-Kaup-Newell-Segur (AKNS) equation vanish on all pairs of formal Laurent series of a specified form, both of them with a pole of the first order. We propose a new and very simple proof for this statement, based on the theory of Baecklund transformations; using the same method, we prove that the AKNS conserved functionals vanish on other pairs of Laurent series. The spirit is the same of our previous paper on the Treves theorem for the KdV equation (J.Math.Phys. 45 (2004) 3558-3564), with some non trivial technical differences.File in questo prodotto:
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