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- W79136418 abstract "In the last decade much progress has been made in the theory of integrable nonlinear partial differential equations (PDE’s) [1, 2]. The inverse scattering formalism provides an exact linearization in the sense that the initial value problem of the PDE is reduced to solving linear problems. In fact, for suitable boundary conditions the time evolution of the scattering data is governed by linear relations, so that the solutions of the PDE can be obtained with the help of a Gel’fand-Levitan equation. Recently, however, FOKAS and ABLOWITZ [3] have proposed a direct method of exact linearization for the Korteweg-de Vries equation, which is based on a linear integral equation having an arbitrary measure and contour. Since then various other PDE’s have been treated as well [4,5,6] and it has been shown that Backlund transformations can be generated by an appropriate transformation of the measure or the source term in the integral equation [7,8]." @default.
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- W79136418 date "1984-01-01" @default.
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- W79136418 title "Solitons in Lattice Systems" @default.
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