Scattering theory for higher order equations


This paper deals with scattering theory for equations of the form where M = 2N with N a positive integer, and {Bk} are M commuting, skew-adjoint operators on a Hilbert space H. It has been shown [3] that equations of this form may be written f where A is a skew-adjoint, M by M matrix of operators on the Hilbert space HM. This matrix will be shown to be unitarily equivalent to the M x M diagonal matrix with the operators {Bk} on the diagonal. If {Bkn}, n = 0, 1, are two families of commuting, skew-adjoint operators on H, let An, n = 0, 1, be the matrices of operators on HM corresponding to { Bkn}, n = 0, 1. It will be shown that the wave operats Ω ±(iB1k, iB0k) on H exist (and are complete) for k= 1, 2, …, M, if and only if the wave operators Ω± (iA1, iA0) exist (and are complete). This result will be applied to the equations of linear elasticity. © 1990, Khayyam Publishing. All rights reserved.

Publication Title

Differential and Integral Equations

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