An infinite number of conservation laws for coupled nonlinear evolution equations

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Abstract
The n‐dimensional Zakharov‐Shabat eigenvalue problem and the corresponding time dependencey of the vector eigenfuncions are considered. It is known that certain coupled systems of nonlinear partial differential equatons are equivalent to the time invariance of the spectrum. Here, for any such coupled system, and infinite sequence of conservation laws is explicitly derived. As an example, this result is applied to the equaions describing three resonantly interacting nonlinear wave envelopes.