According to a theorem of Treves (Duke Math. Journal 108 (2001), 251-294), the conserved functionals of the KdV equation vanish on each formal Laurent series of the form 1/x^2 + u0 + u2 x^2 + u3 x^3 + >... . The proof given by Treves is rather long: in this paper we propose a new, very simple geometrical proof for this statement, stemming from the remark that the KdV functionals are invariant under Baecklund transformations obtained by composing Miura and reflection transformations.
On a theorem by Treves
MOROSI, CARLO;
2004-01-01
Abstract
According to a theorem of Treves (Duke Math. Journal 108 (2001), 251-294), the conserved functionals of the KdV equation vanish on each formal Laurent series of the form 1/x^2 + u0 + u2 x^2 + u3 x^3 + >... . The proof given by Treves is rather long: in this paper we propose a new, very simple geometrical proof for this statement, stemming from the remark that the KdV functionals are invariant under Baecklund transformations obtained by composing Miura and reflection transformations.File in questo prodotto:
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