UNIVERSAL AND INTEGRABLE NONLINEAR EVOLUTION SYSTEMS OF EQUATIONS IN 2-1-1 DIMENSIONS

Integrable systems of nonlinear partial differential equations (PDEs) are obtained from integrable equations in 2 + 1 dimensions, by means o f a reduction method of broad applicability based on Fourier expansion and spatio-temporal rescalings, which is asymptotically exact in the limit of weak nonlinearity. The integrability by the spectral transfor m is explicitly demonstrated, because the corresponding Lax pairs have been derived, applying the same reduction method to the Lax pair of t he initial equation. These systems of nonlinear PDEs are likely to be of applicative relevance and have a ''universal'' character, inasmuch as they may be derived from a very large class of nonlinear evolution equations with a linear dispersive part. (C) 1997 American Institute o f Physics.