Integrable nonlinear evolution equations with constraints: I

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Abstract
The author presents a general method to construct classes of integrable nonlinear evolution equations in n+1 dimensions (n in N) with constraints. The constraint is given by a set of, in general nonlinear, equations and is equivalent to a generalized commutativity condition for a finite number of linear operators. As an application of the method he generates several examples of nonlinear evolution equations with constraints; some of them are integrable through a change of variables (like an (n+1)-dimensional generalization of the Burgers equation), others through a more complicated transformation, involving the solution of a delta problem.