T.V. Redkina, A.I. Karyuk, G.A. Lushnikova

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The construction of non-linear equations, which have as the operator of diffusement L : Dirac's operator, the first-rate operator with matrix factors 2x2 and 3x3 is demonstrated in the article. The new system of non-linear in private derivatives, which has an equation on its own value with Dirac's operator, is got 1+1 and 2+1-dimensional equations, which possess common task on their own values and different operators A are got. Non-linear equation in private derivatives with the third-rate diffusement operator is found. For the equations given in the article the precise solutions of special kind are found.