Linearizing Integral Transform and Partial Difference Equations
نویسندگان
چکیده
A linearizing integral transform is proposed which relates solutions of a spectral problem associated with a class of inte-grable partial difference equations to any given solution of the spectral problem. Examples of this class are lattice versions of the isotropic Heisenberg spin chain, the nonlinear SchrSdinger equation and the (complex) sine-Gordon equation. 1. Introduction. Recently a direct linearization method which is based on the use of linear integral equations with singular kernels and arbitrary measures and contours has been developed to obtain solutions of integrable nonlinear systems [ 1-3]. The integral equations which connect nontrivial solutions of a spectral problem associated with an integrable nonlinear system to so-called free-reference solutions (i.e. solutions of the spectral problem associated with a trivial potential), can be related to the well-known Riemann-Hilbert transformations in special cases [4]. Very recently a generalization of this approach was formulated on the basis of linearizing integral transforms which transform any given solution of the spectral problem into another solution of the same spectral problem [5-7]. This generalization may be regarded as being reminiscent of earlier work relating different solutions of the spectral problem via a Gel'fand-Levitan equation [8-10]. In this note we extend this approach to study the
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تاریخ انتشار 2002