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The Inverse Scattering Method and Systems of Equations qxy = F(q, qy)

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Consider equations of the form where q is in general a complex vector and the function F depends nontrivially both on q and on qy . We show that a family S of such equations can be investigated by the inverse scattering method. If an equation (*) belongs to S, the function F depends linearly on q and algebraically on qy . We show that the family S contains a subfamily in which each equation can be obtained from the two dimensional Toda lattice equations by a Bäcklund transformation.
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Document Type: Research Article

Affiliations: Yale University Universitè de Nantes

Publication date: July 1, 1994

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