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The Inverse Scattering Method and Systems of Equations q xy = F ( q, q y )
Author(s) -
Beals Richard,
Nouikou Roman G.
Publication year - 1994
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm1994923201
Subject(s) - mathematics , inverse , subfamily , scattering , lattice (music) , mathematical physics , mathematical analysis , function (biology) , inverse scattering problem , transformation (genetics) , toda lattice , pure mathematics , inverse problem , physics , quantum mechanics , geometry , integrable system , chemistry , biochemistry , evolutionary biology , biology , acoustics , gene
Consider equations of the form where q is in general a complex vector and the function F depends nontrivially both on q and on q y . 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 q y . 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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