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Basic Aspects of Solition Theory
This is a review of the main ideas of the inverse scattering method (ISM) for solving nonlinear evolution equations (NLEE), known as soliton equations. As a basic tool we use the fundamental analytic solutions χ ± (x, λ) of the Lax operator L(λ). Then the inverse scattering problem for L(λ) reduces to a Riemann-Hilbert problem. Such construction has been applied to wide class of Lax operators, related to the simple Lie algebras. We construct the kernel of the resolvent of L(λ) in terms of χ ±doi:10.7546/giq-6-2005-78-125 fatcat:pw5pz2wopvahvjigewe5qtw56i