Some new nonlinear evolution equations integrable by the inverse problem method

Several new nonlinear evolution equations integrable by the inverse problem method are obtained. The method applied in finding these equations is believed to be essentially new. The comparison of that method with other methods for finding nonlinear evolution equations integrable by the inverse problem method is given. In particular, it is shown that the methods using the Heisenberg equation (the so-called Lax representation) are not suitable to obtain the equations studied here.
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