Geodesic
Model equation of the theory of solitons
Teoretičeskaâ i matematičeskaâ fizika, Tome 153 (2007) no. 1, pp. 29-45 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the hierarchy of integrable $(1+2)$-dimensional equations related to the Lie algebra of vector fields on the line. We construct solutions in quadratures that contain $n$ arbitrary functions of a single argument. A simple equation for the generating function of the hierarchy, which determines the dynamics in negative times and finds applications to second-order spectral problems, is of main interest. Considering its polynomial solutions under the condition that the corresponding potential is regular allows developing a rather general theory of integrable $(1+1)$-dimensional equations.
Keywords: hierarchy of commuting vector fields
Mots-clés : Riemann invariant, Dubrovin equations. 
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V. E. Adler; A. B. Shabat. Model equation of the theory of solitons. Teoretičeskaâ i matematičeskaâ fizika, Tome 153 (2007) no. 1, pp. 29-45. http://geodesic.mathdoc.fr/item/TMF_2007_153_1_a2/

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