Abstract
We present a class of nonlinear Klein-Gordon systems which are soluble by means of a scattering transform. More specifically, for eachN≧2 we present a system of (N−1) nonlinear Klein-Gordon equations, together with the correspondingN ×N matrix scattering problem which can be used to solve it. We illustrate these with some special examples. The general system is shown to be closely related to the equations of the periodic Toda lattice. We present a Bäcklund transformation and superposition formula for the general system.
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Communicated by J. Moser
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Fordy, A.P., Gibbons, J. Integrable nonlinear Klein-Gordon equations and Toda lattices. Commun.Math. Phys. 77, 21–30 (1980). https://doi.org/10.1007/BF01205037
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DOI: https://doi.org/10.1007/BF01205037