Abstract
In this paper we show that the Darboux transformation for a large class of nonlinear evolution equations arises due to factorization and commutation. The factorization and commutation has been pointed out earlier for Schrodinger operator. We show that it extends to a large class of nonlinear differential equations which admit Lax pairs including Boussinesq, Davey–Stewartson, Bogoyavlensky–Schiff and n-wave interaction equation.
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