Abstract
It is pointed out that the linear scattering problem for a non-linear evolution equation which admits soliton solutions may be described in terms of a linear connection on a principal SL(2, ℝ). The equation in question is satisfied if and only if the curvature of this connection vanishes. Some other properties of the curvature are identified. The sine-Gordon, Korteweg-de Vries and modified Korteweg-de Vries equations are treated explicitly.
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